{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,16]],"date-time":"2026-02-16T20:58:50Z","timestamp":1771275530816,"version":"3.50.1"},"reference-count":130,"publisher":"Elsevier","isbn-type":[{"value":"9780444527264","type":"print"}],"license":[{"start":{"date-parts":[[2006,1,1]],"date-time":"2006-01-01T00:00:00Z","timestamp":1136073600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2006,1,1]],"date-time":"2006-01-01T00:00:00Z","timestamp":1136073600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2006]]},"DOI":"10.1016\/s1574-6526(06)80020-9","type":"book-chapter","created":{"date-parts":[[2008,2,26]],"date-time":"2008-02-26T16:51:39Z","timestamp":1204044699000},"page":"571-603","source":"Crossref","is-referenced-by-count":67,"title":["Continuous and Interval Constraints"],"prefix":"10.1016","member":"78","reference":[{"key":"10.1016\/S1574-6526(06)80020-9_bib1","series-title":"Introduction to Interval Computations","author":"Alefeld","year":"1983"},{"issue":"1\u20132","key":"10.1016\/S1574-6526(06)80020-9_bib2","first-page":"179","article-title":"The Essence of Constraint Propagation","volume":"221","author":"Krzysztof","year":"1999","journal-title":"Theoretical Computer Science"},{"key":"10.1016\/S1574-6526(06)80020-9_bib3","series-title":"Proceedings of International Conference on Principles and Practice of Constraint Programming","first-page":"77","article-title":"Mind the Gaps: A New Splitting Strategy for Consistency Techniques","volume":"volume 3709","author":"Batnini","year":"2005"},{"key":"10.1016\/S1574-6526(06)80020-9_bib4","series-title":"Proceedings of International Conference on Principles and Practice of Constraint Programming","first-page":"67","article-title":"Universally Quantified Interval Constraints","volume":"volume 1894","author":"Benhamou","year":"2000"},{"issue":"3","key":"10.1016\/S1574-6526(06)80020-9_bib5","doi-asserted-by":"crossref","first-page":"335","DOI":"10.1023\/A:1009943413814","article-title":"Automatic Generation of Numerical Redundancies for Non-Linear Constraint Solving","volume":"3","author":"Benhamou","year":"1997","journal-title":"Reliable Computing"},{"issue":"1","key":"10.1016\/S1574-6526(06)80020-9_bib6","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/S0743-1066(96)00142-2","article-title":"Applying Interval Arithmetic to Real, Integer and Boolean Constraints","volume":"32","author":"Benhamou","year":"1997","journal-title":"Journal of Logic Programming"},{"key":"10.1016\/S1574-6526(06)80020-9_bib7","series-title":"Journ\u00e9es Francophones de Programmation en Logique","first-page":"51","article-title":"Prolog IV: Langage et Algorithmes","author":"Benhamou","year":"1995"},{"key":"10.1016\/S1574-6526(06)80020-9_bib8","series-title":"Proceedings of International Symposium on Logic Programming","first-page":"124","article-title":"CLP(Intervals) Revisited","author":"Benhamou","year":"1994"},{"key":"10.1016\/S1574-6526(06)80020-9_bib9","series-title":"Proceedings of International Conference on Logic Programming","first-page":"230","article-title":"Revising Hull and Box Consistency","author":"Benhamou","year":"1999"},{"issue":"4","key":"10.1016\/S1574-6526(06)80020-9_bib10","doi-asserted-by":"crossref","first-page":"732","DOI":"10.1145\/1024922.1024927","article-title":"Interval Constraint Solving for Camera Control and Motion Planning","volume":"5","author":"Benhamou","year":"2004","journal-title":"ACM Transactions on Computational Logic"},{"key":"10.1016\/S1574-6526(06)80020-9_bib11","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1023\/A:1009958918582","article-title":"Computation and Application of Taylor Polynomials with Interval Remainder Bounds","volume":"4","author":"Berz","year":"1998","journal-title":"Reliable Computing"},{"key":"10.1016\/S1574-6526(06)80020-9_bib12","series-title":"Proceedings of International Conference on Principles and Practice of Constraint Programming","first-page":"102","article-title":"Using Graph Decomposition for Solving Continuous CSPs","volume":"volume 1520","author":"Bliek","year":"1998"},{"key":"10.1016\/S1574-6526(06)80020-9_bib13","first-page":"752","article-title":"Handbook of Automated Reasoning, chapter Solving Numerical Constraints","author":"Bockmayr","year":"2001"},{"key":"10.1016\/S1574-6526(06)80020-9_bib14","article-title":"The Boost Interval Arithmetic Library","author":"Br\u00f6nnimann","year":"2006","journal-title":"Theoretical Computer Science, Special Issue on Real Numbers and Computers"},{"key":"10.1016\/S1574-6526(06)80020-9_bib15","first-page":"97","article-title":"\u00dcber Abbildung von Mannigfaltigkeiten","volume":"71","author":"Egbertus","year":"1912","journal-title":"Mathematische Annalen"},{"key":"10.1016\/S1574-6526(06)80020-9_bib16","series-title":"Multidimensional Systems Theory","first-page":"184","article-title":"Gr\u00f6bner Bases: an Algorithmic Method in Polynomial Ideal Theory","author":"Buchberger","year":"1985"},{"key":"10.1016\/S1574-6526(06)80020-9_bib17","doi-asserted-by":"crossref","first-page":"147","DOI":"10.1007\/BF02259640","article-title":"Mean Value Forms in Interval Analysis","volume":"25","author":"Caprani","year":"1980","journal-title":"Computing"},{"issue":"1","key":"10.1016\/S1574-6526(06)80020-9_bib18","doi-asserted-by":"crossref","first-page":"51","DOI":"10.1007\/s00607-002-1448-y","article-title":"Horner's Rule for Interval Evaluation Revisited","volume":"69","author":"Ceberio","year":"2002","journal-title":"Computing"},{"issue":"6","key":"10.1016\/S1574-6526(06)80020-9_bib19","doi-asserted-by":"crossref","first-page":"615","DOI":"10.1177\/0278364904044079","article-title":"An Interval Analysis Based Study for the Design and the Comparison of 3-DOF Parallel Kinematic Machines","volume":"23","author":"Chablat","year":"2004","journal-title":"International Journal of Robotics Research"},{"key":"10.1016\/S1574-6526(06)80020-9_bib20","series-title":"Proceedings of the Annual Eurographics Conference","first-page":"247","article-title":"A Semantic Space Partitionning Approach to Virtual Camera Control","volume":"volume 24","author":"Christie","year":"2005"},{"issue":"2","key":"10.1016\/S1574-6526(06)80020-9_bib21","first-page":"125","article-title":"Logical Arithmetic","volume":"2","author":"Cleary","year":"1987","journal-title":"Future Computing Systems"},{"key":"10.1016\/S1574-6526(06)80020-9_bib22","series-title":"Proceedings of International Joint Conference on Artificial Intelligence","first-page":"406","article-title":"Extending Consistent Domains of Numeric CSPs","author":"Collavizza","year":"1999"},{"issue":"3","key":"10.1016\/S1574-6526(06)80020-9_bib23","doi-asserted-by":"crossref","first-page":"213","DOI":"10.1023\/A:1009922003700","article-title":"Comparing partial consistencies","volume":"5","author":"Collavizza","year":"1999","journal-title":"Reliable Computing"},{"key":"10.1016\/S1574-6526(06)80020-9_bib24","series-title":"Proceedings of the 2nd GI Conference on Automata Theory and Formal Languages","first-page":"134","article-title":"Quantifier elimination for real closed fields by cylindrical algebraic decomposition","author":"Collins","year":"1975"},{"key":"10.1016\/S1574-6526(06)80020-9_bib25","doi-asserted-by":"crossref","first-page":"299","DOI":"10.1016\/S0747-7171(08)80152-6","article-title":"Partial Cylindrical Algebraic Decomposition for Quantifier Elimination","volume":"12","author":"Collins","year":"1991","journal-title":"Journal of Symbolic Computation"},{"issue":"7","key":"10.1016\/S1574-6526(06)80020-9_bib26","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1145\/79204.79210","article-title":"An Introduction to Prolog III","volume":"33","author":"Colmerauer","year":"1990","journal-title":"Communications of the ACM"},{"key":"10.1016\/S1574-6526(06)80020-9_bib27","series-title":"Proceedings of International Conference on Fifth Generation Computer Systems","first-page":"85","article-title":"Equations and Inequations on Finite and Infinite Trees","author":"Colmerauer","year":"1984"},{"key":"10.1016\/S1574-6526(06)80020-9_bib28","series-title":"Proceedings of International Conference on Principles and Practice of Constraint Programming","first-page":"259","article-title":"Constraint Satisfaction Differential Problems","volume":"volume 2833","author":"Cruz","year":"2003"},{"key":"10.1016\/S1574-6526(06)80020-9_bib29","series-title":"Proceedings of Portuguese Conference on Artificial Intelligence","first-page":"349","article-title":"Global Hull Consistency with Local Search for Continuous Constraint Solving","volume":"volume 2258","author":"Cruz","year":"2001"},{"issue":"3","key":"10.1016\/S1574-6526(06)80020-9_bib30","doi-asserted-by":"crossref","first-page":"922","DOI":"10.1137\/S0036142995281528","article-title":"Subdivision Direction Selection in Interval Mathods for Global Optimization","volume":"34","author":"Csendes","year":"1997","journal-title":"SIAM Journal on Numerical Analysis"},{"key":"10.1016\/S1574-6526(06)80020-9_bib31","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1016\/S0747-7171(88)80004-X","article-title":"Real quantifier elimination is doubly exponential","volume":"5","author":"Davenport","year":"1988","journal-title":"Journal of Symbolic Computation"},{"key":"10.1016\/S1574-6526(06)80020-9_bib32","doi-asserted-by":"crossref","first-page":"281","DOI":"10.1016\/0004-3702(87)90091-9","article-title":"Constraint Propagation with Interval Labels","volume":"32","author":"Davis","year":"1987","journal-title":"Artificial Intelligence"},{"issue":"5","key":"10.1016\/S1574-6526(06)80020-9_bib33","doi-asserted-by":"crossref","first-page":"287","DOI":"10.1111\/1467-8659.1550287","article-title":"Adaptive Enumeration of Implicit Surfaces with Affine Arithmetic","volume":"15","author":"de Figueiredo","year":"1996","journal-title":"Computer Graphics Forum"},{"key":"10.1016\/S1574-6526(06)80020-9_bib34","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/0004-3702(87)90002-6","article-title":"Network-based Heuristics for Constraint Satisfaction Problems","volume":"34","author":"Dechter","year":"1988","journal-title":"Artificial Intelligence"},{"key":"10.1016\/S1574-6526(06)80020-9_bib35","series-title":"Proceedings of International Workshop on Practical Aspects of Declarative Languages","first-page":"81","article-title":"GNU Prolog: Beyond Compiling Prolog to C","volume":"volume 1753","author":"Diaz","year":"2000"},{"key":"10.1016\/S1574-6526(06)80020-9_bib36","series-title":"Institute for New Generation Computer Technology, Proceedings of International Conference on Fifth Generation Computer Systems","first-page":"693","article-title":"The constraint logic programming language chip","author":"Dincbas","year":"1988"},{"issue":"2","key":"10.1016\/S1574-6526(06)80020-9_bib37","doi-asserted-by":"crossref","first-page":"363","DOI":"10.1016\/0004-3702(94)90022-1","article-title":"Arc Consistency for Continuous Variables","volume":"65","author":"Faltings","year":"1994","journal-title":"Artificial Intelligence"},{"key":"10.1016\/S1574-6526(06)80020-9_bib38","series-title":"Proceedings of International Joint Conference on Artificial Intelligence","first-page":"392","article-title":"Local Consistency for Ternary Numeric Constraints","author":"Faltings","year":"1997"},{"issue":"11","key":"10.1016\/S1574-6526(06)80020-9_bib39","doi-asserted-by":"crossref","first-page":"958","DOI":"10.1145\/359642.359654","article-title":"Synthesizing Constraint Expressions","volume":"21","author":"Freuder","year":"1978","journal-title":"Communications of the ACM"},{"key":"10.1016\/S1574-6526(06)80020-9_bib40","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1145\/322290.322292","article-title":"A sufficient condition for backtrack-free search","volume":"29","author":"Freuder","year":"1982","journal-title":"Journal of the ACM"},{"key":"10.1016\/S1574-6526(06)80020-9_bib41","doi-asserted-by":"crossref","first-page":"349","DOI":"10.1007\/s00607-004-0064-4","article-title":"A Comparison of the Moore and Miranda Existence Tests","volume":"72","author":"Frommer","year":"2004","journal-title":"Computing"},{"issue":"2","key":"10.1016\/S1574-6526(06)80020-9_bib42","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1023\/A:1011465930178","article-title":"Modal intervals","volume":"7","author":"Gardenes","year":"2001","journal-title":"Reliable Computing"},{"key":"10.1016\/S1574-6526(06)80020-9_bib43","series-title":"Symbolic Methods in Control System Analysis and Design","first-page":"339","article-title":"Solving Strict Polynomial Inequalities by Bernstein Expansion","author":"Garloff","year":"1999"},{"key":"10.1016\/S1574-6526(06)80020-9_bib44","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1023\/A:1022394531132","article-title":"Solving Mixed and Conditional Constraint Satisfaction Problems","volume":"8","author":"Gelle","year":"2003","journal-title":"Constraints"},{"key":"10.1016\/S1574-6526(06)80020-9_bib45","series-title":"Proceedings of Annual Conference on Computer Graphics and Interactive Techniques","first-page":"331","article-title":"Through-the-lens Camera Control","author":"Gleicher","year":"1992"},{"key":"10.1016\/S1574-6526(06)80020-9_bib46","article-title":"D\u00e9finition et Applications des Extensions des Fonctions R\u00e9elles aux Intervalles G\u00e9n\u00e9ralis\u00e9s: Nouvelle Formulation de la Th\u00e9orie des Intervalles Modaux et Nouveaux R\u00e9sultats","author":"Goldsztejn","year":"2005","journal-title":"PhD thesis, Universit\u00e9 de Nice"},{"key":"10.1016\/S1574-6526(06)80020-9_bib47","series-title":"Gaol: NOT Just Another Interval Library","author":"Goualard","year":"2005"},{"key":"10.1016\/S1574-6526(06)80020-9_bib48","series-title":"Proceedings of ACM Symposium of Applied Computing","first-page":"31434","article-title":"On Considering an Interval Constraint Solving Algorithm as a Free-steering Nonlinear Gauss-Seidel Procedure","author":"Goualard","year":"2005"},{"key":"10.1016\/S1574-6526(06)80020-9_bib49","series-title":"Proceedings of ACM Symposium of Applied Computing","first-page":"377","article-title":"Controlled Propagation in Continuous Numerical Constraint Networks","author":"Goualard","year":"2005"},{"issue":"1","key":"10.1016\/S1574-6526(06)80020-9_bib50","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1016\/j.cam.2003.08.022","article-title":"An Interval Component for Continuous Constraints","volume":"162","author":"Granvilliers","year":"2004","journal-title":"Journal of Computational and Applied Mathematics"},{"issue":"6","key":"10.1016\/S1574-6526(06)80020-9_bib51","doi-asserted-by":"crossref","first-page":"467","DOI":"10.1023\/A:1014750702474","article-title":"On the Combination of Interval Constraint Solvers","volume":"7","author":"Granvilliers","year":"2001","journal-title":"Reliable Computing"},{"issue":"2","key":"10.1016\/S1574-6526(06)80020-9_bib52","doi-asserted-by":"crossref","first-page":"155","DOI":"10.1023\/A:1011266226870","article-title":"Progress in the Solving of a Circuit Design Problem","volume":"20","author":"Granvilliers","year":"2001","journal-title":"Journal of Global Optimization"},{"key":"10.1016\/S1574-6526(06)80020-9_bib53","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1016\/S0020-0190(00)00048-X","article-title":"A Conservative Scheme for Parallel Interval Narrowing","volume":"74","author":"Granvilliers","year":"2000","journal-title":"Information Processing Letters"},{"key":"10.1016\/S1574-6526(06)80020-9_bib54","series-title":"Proceedings of International Conference on Logic Programming, volume 2916 of Lecture Notes in Computer Science","first-page":"300","article-title":"Implementing Constraint Propagation by Composition of Reductions","author":"Granvilliers","year":"2003"},{"key":"10.1016\/S1574-6526(06)80020-9_bib55","series-title":"Proceedings of International Conference on Artificial Intelligence and Symbolic Computation","first-page":"118","article-title":"Combination of Nonlinear Terms in Interval Constraint Satisfaction Techniques","volume":"volume 3249","author":"Granvilliers","year":"2004"},{"key":"10.1016\/S1574-6526(06)80020-9_bib56","series-title":"Proceedings of IEEE Conference on Tools with Artificial Intelligence","first-page":"373","article-title":"Box Consistency through Weak Box Consistency","author":"Granvilliers","year":"1999"},{"key":"10.1016\/S1574-6526(06)80020-9_bib57","series-title":"Proceedings of International Symposium on Symbolic and Algebraic Computation","first-page":"150","article-title":"Symbolic-Interval Cooperation in Constraint Programming","author":"Granvilliers","year":"2001"},{"key":"10.1016\/S1574-6526(06)80020-9_bib58","series-title":"Numerical Software with Result Verification, volume 2991 of Lecture Notes in Computer Science","first-page":"64","article-title":"Multiple Precision Interval Packages: Comparing Different Approaches","author":"Grimmer","year":"2004"},{"key":"10.1016\/S1574-6526(06)80020-9_bib59","series-title":"Proceedings of Workshop on Applications of Interval Analysis to Systems and Control","first-page":"139","article-title":"Modal Intervals","year":"1999"},{"key":"10.1016\/S1574-6526(06)80020-9_bib60","article-title":"C++ Toolbox for Verified Computing","author":"Hammer","year":"1995"},{"key":"10.1016\/S1574-6526(06)80020-9_bib61","series-title":"Global Optimization using Interval Analysis","author":"Hansen","year":"1992"},{"key":"10.1016\/S1574-6526(06)80020-9_bib62","first-page":"308","article-title":"Interval Arithmetic in Matrix Computations","volume":"2","author":"Hansen","year":"1965","journal-title":"SIAM Journal of Numerical Analysis"},{"issue":"2","key":"10.1016\/S1574-6526(06)80020-9_bib63","doi-asserted-by":"crossref","first-page":"203","DOI":"10.1007\/BF01933165","article-title":"Bounding Solutions of Systems of Equations using Interval Analysis","volume":"21","author":"Hansen","year":"1981","journal-title":"BIT"},{"issue":"5","key":"10.1016\/S1574-6526(06)80020-9_bib64","doi-asserted-by":"crossref","first-page":"1038","DOI":"10.1145\/502102.502106","article-title":"Interval Arithmetic: From Principles to Implementation","volume":"48","author":"Hickey","year":"2001","journal-title":"Journal of the ACM"},{"key":"10.1016\/S1574-6526(06)80020-9_bib65","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1007\/BF02238236","article-title":"Bernstein Form is Inclusion Monotone","volume":"55","author":"Hong","year":"1995","journal-title":"Computing"},{"key":"10.1016\/S1574-6526(06)80020-9_bib66","series-title":"Proceedings of Annual ACM Symposium on User Interface Software and Technology","first-page":"91","article-title":"A Modular Geometric Constraint Solver for User Interface Applications","author":"Hosobe","year":"2001"},{"key":"10.1016\/S1574-6526(06)80020-9_bib67","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1016\/0004-3702(92)90005-I","article-title":"Constraint Reasoning based on Interval Arithmetic. The Tolerance Propagation Approach","volume":"58","author":"Hyv\u00f6nen","year":"1992","journal-title":"Artificial Intelligence"},{"key":"10.1016\/S1574-6526(06)80020-9_bib68","series-title":"Proceedings of International Joint Conference on Artificial Intelligence","first-page":"1193","article-title":"Constraint Reasoning Based on Interval Arithmetic","author":"Hyv\u00f6nen","year":"1989"},{"key":"10.1016\/S1574-6526(06)80020-9_bib69","series-title":"IEEE Standard for Binary Floating-Point Arithmetic","author":"IEEE","year":"1985"},{"key":"10.1016\/S1574-6526(06)80020-9_bib70","series-title":"Proceedings of ACM Symposium on Principles of Programming Languages","first-page":"111","article-title":"Constraint Logic Programming","author":"Jaffar","year":"1987"},{"key":"10.1016\/S1574-6526(06)80020-9_bib71","doi-asserted-by":"crossref","first-page":"503","DOI":"10.1016\/0743-1066(94)90033-7","article-title":"Constraint Logic Programming: A Survey","volume":"19\u201320","author":"Jaffar","year":"1994","journal-title":"Journal of Logic Programming"},{"issue":"3","key":"10.1016\/S1574-6526(06)80020-9_bib72","doi-asserted-by":"crossref","first-page":"339","DOI":"10.1145\/129393.129398","article-title":"The CLP(o) language and system","volume":"14","author":"Jaffar","year":"1992","journal-title":"ACM Transactions on Programming Languages and Systems"},{"issue":"5","key":"10.1016\/S1574-6526(06)80020-9_bib73","doi-asserted-by":"crossref","first-page":"1896","DOI":"10.1137\/S0036142901392316","article-title":"A Constraint Satisfaction Approach for Enclosing Solutions to Parametric Ordinary Differential Equations","volume":"40","author":"Janssen","year":"2002","journal-title":"SIAM Journal on Numerical Analysis"},{"issue":"3","key":"10.1016\/S1574-6526(06)80020-9_bib74","doi-asserted-by":"crossref","first-page":"914","DOI":"10.1137\/S1052623402416839","article-title":"Rigorous Lower and Upper Bounds in Linear Programming","volume":"14","author":"Jansson","year":"2004","journal-title":"SIAM Journal on Optimization"},{"key":"10.1016\/S1574-6526(06)80020-9_bib75","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1007\/BF02331571","article-title":"Rigorous Solution of Linear Programming Problems with Uncertain Data","volume":"35","author":"Jansson","year":"1991","journal-title":"Methods and Models of Operations Research"},{"issue":"3","key":"10.1016\/S1574-6526(06)80020-9_bib76","doi-asserted-by":"crossref","first-page":"175","DOI":"10.1111\/1467-8659.00265","article-title":"Screen-space constraints for camera movements: the virtual cameraman","volume":"17","author":"Jardillier","year":"1998","journal-title":"Computer Graphics Forum"},{"issue":"4","key":"10.1016\/S1574-6526(06)80020-9_bib77","doi-asserted-by":"crossref","first-page":"1053","DOI":"10.1016\/0005-1098(93)90106-4","article-title":"Set Inversion via Interval Analysis for Nonlinear Bounded-Error Estimation","volume":"29","author":"Jaulin","year":"1993","journal-title":"Automatica"},{"issue":"9","key":"10.1016\/S1574-6526(06)80020-9_bib78","doi-asserted-by":"crossref","first-page":"1217","DOI":"10.1016\/0005-1098(96)00050-7","article-title":"Guaranteed tuning, with application to robust control and motion planning","volume":"32","author":"Jaulin","year":"1996","journal-title":"Automatica"},{"key":"10.1016\/S1574-6526(06)80020-9_bib79","series-title":"Applied Interval Analysis: With Examples in Parameter and State Estimation, Robust Control and Robotics","author":"Jaulin","year":"2001"},{"key":"10.1016\/S1574-6526(06)80020-9_bib80","article-title":"A More Complete Interval Arithmetic","author":"Kahan","year":"1968"},{"key":"10.1016\/S1574-6526(06)80020-9_bib81","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1007\/978-3-7091-8577-3_3","article-title":"Interval Analysis in the Extended Interval Space IR","volume":"2","author":"Kaucher","year":"1980","journal-title":"Computing Supplementum"},{"key":"10.1016\/S1574-6526(06)80020-9_bib82","series-title":"Nonconvex Optimization and Its Applications","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4757-2495-0","article-title":"Rigorous Global Search: Continuous Problems","author":"Keafott","year":"1996"},{"key":"10.1016\/S1574-6526(06)80020-9_bib83","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1007\/BF02234767","article-title":"Newton-Algorithmen zur Bestimmung von Nullstellen mit Fehlerschranken","volume":"4","author":"Krawczyk","year":"1969","journal-title":"Computing"},{"key":"10.1016\/S1574-6526(06)80020-9_bib84","series-title":"Proceedings of International Conference on Principles and Practice of Constraint Programming, volume 1713 of Lecture Notes in Computer Science","first-page":"289","article-title":"Applying Constraint Programming to Protein Structure Determination","author":"Krippahl","year":"1999"},{"key":"10.1016\/S1574-6526(06)80020-9_bib85","series-title":"Proceedings of International Workshop on Techniques for Implementing Constraint Programming Systems","article-title":"CHOCO: implementing a CP kernel","author":"Laburthe","year":"2000"},{"issue":"1","key":"10.1016\/S1574-6526(06)80020-9_bib86","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1016\/S0004-3702(02)00194-7","article-title":"Accelerating Filtering Techniques for Numeric CSPs","volume":"139","author":"Lebbah","year":"2002","journal-title":"Artificial Intelligence"},{"issue":"5","key":"10.1016\/S1574-6526(06)80020-9_bib87","doi-asserted-by":"crossref","first-page":"2076","DOI":"10.1137\/S0036142903436174","article-title":"Efficient and Safe Global Constraints for handling Numerical Constraint Systems","volume":"42","author":"Lebbah","year":"2005","journal-title":"SIAM Journal on Numerical Analysis"},{"key":"10.1016\/S1574-6526(06)80020-9_bib88","series-title":"Proceedings of International Joint Conference on Artificial Intelligence","first-page":"232","article-title":"Consistency Techniques for Numeric CSPs","author":"Lhomme","year":"1993"},{"issue":"1\u20132","key":"10.1016\/S1574-6526(06)80020-9_bib89","doi-asserted-by":"crossref","first-page":"165","DOI":"10.1016\/S0743-1066(98)10007-9","article-title":"Dynamic Optimization of Interval Narrowing Algorithms","volume":"37","author":"Lhomme","year":"1998","journal-title":"Journal of Logic Programming"},{"issue":"1","key":"10.1016\/S1574-6526(06)80020-9_bib90","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1016\/0004-3702(77)90007-8","article-title":"Consistency in Networks of Relations","volume":"8","author":"Mackworth","year":"1977","journal-title":"Artificial Intelligence"},{"issue":"1\u20132","key":"10.1016\/S1574-6526(06)80020-9_bib91","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1142\/S0218213095000061","article-title":"A Distributed Cooperating Constraints Solving System","volume":"4","author":"Marti","year":"1995","journal-title":"International Journal on Artificial Intelligence Tools"},{"issue":"3","key":"10.1016\/S1574-6526(06)80020-9_bib92","doi-asserted-by":"crossref","first-page":"221","DOI":"10.1177\/0278364904039806","article-title":"Solving the Forward Kinematics of a Gough-type Parallel Manipulator with Interval Analysis","volume":"23","author":"Merlet","year":"2004","journal-title":"International Journal of Robotics Research"},{"issue":"11","key":"10.1016\/S1574-6526(06)80020-9_bib93","first-page":"992","article-title":"Extensions of Affine Arithmetic: Application to Global Optimization","volume":"8","author":"Messine","year":"2002","journal-title":"Journal of Universal Computer Science"},{"issue":"2","key":"10.1016\/S1574-6526(06)80020-9_bib94","first-page":"5","article-title":"Un'osservatione su un teorema di Brouwer","volume":"3","author":"Miranda","year":"1940","journal-title":"Boll. Un. Mat. Ital."},{"key":"10.1016\/S1574-6526(06)80020-9_bib95","series-title":"Proceedings of ACM Symposium on Applied Computing","first-page":"63","article-title":"Implementing Non-Linear Constraints with Cooperative Solvers","author":"Monfroy","year":"1996"},{"issue":"2","key":"10.1016\/S1574-6526(06)80020-9_bib96","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1016\/0020-0255(74)90008-5","article-title":"Networks of Constraints: Fundamental Properties and Applications to Picture Processing","volume":"7","author":"Montanari","year":"1974","journal-title":"Information Science"},{"issue":"2","key":"10.1016\/S1574-6526(06)80020-9_bib97","doi-asserted-by":"crossref","first-page":"143","DOI":"10.1016\/0004-3702(91)90059-S","article-title":"Constraint Relaxation may be Perfect","volume":"48","author":"Montanari","year":"1991","journal-title":"Artificial Intelligence"},{"key":"10.1016\/S1574-6526(06)80020-9_bib98","series-title":"Interval Analysis","author":"Moore","year":"1966"},{"key":"10.1016\/S1574-6526(06)80020-9_bib99","series-title":"Elementary Functions: Algorithms and Implementation","author":"Muller","year":"1997"},{"key":"10.1016\/S1574-6526(06)80020-9_bib100","series-title":"Preprint, USSR academy of sciences, Siberian Division","first-page":"400","article-title":"Subdefinite Models and Operations with Subdefinite Values","author":"Narin'yani","year":"1982"},{"key":"10.1016\/S1574-6526(06)80020-9_bib101","series-title":"Interval Methods for Systems of Equations","author":"Neumaier","year":"1990"},{"key":"10.1016\/S1574-6526(06)80020-9_bib102","doi-asserted-by":"crossref","first-page":"283","DOI":"10.1007\/s10107-003-0433-3","article-title":"Safe Bounds in Linear and Mixed-Integer Programming","volume":"99","author":"Neumaier","year":"2004","journal-title":"Mathematical Programming A"},{"key":"10.1016\/S1574-6526(06)80020-9_bib103","article-title":"On the Newton Method in Interval Analysis","author":"Nickel","year":"1971"},{"key":"10.1016\/S1574-6526(06)80020-9_bib104","series-title":"Proceedings of the first Workshop on Constraint Languages and their Use in Problem Modelling","first-page":"60","article-title":"Application of relational interval arithmetic to ordinary differential equations","author":"Older","year":"1994"},{"key":"10.1016\/S1574-6526(06)80020-9_bib105","series-title":"Proceedings of IEEE Canadian Conference on Electrical and Computer Engineering","article-title":"Extending Prolog with Constraint Arithmetic on Real Intervals","author":"Older","year":"1990"},{"key":"10.1016\/S1574-6526(06)80020-9_bib106","article-title":"Constraint-Aided Conceptual Designs","author":"O'Sullivan","year":"1999","journal-title":"PhD thesis, University College Cork"},{"key":"10.1016\/S1574-6526(06)80020-9_bib107","series-title":"Proceedings of International Symposium of Logic Programming","first-page":"513","article-title":"Beyond the Glass Box: Constraints as Objects","author":"Puget","year":"1995"},{"issue":"1","key":"10.1016\/S1574-6526(06)80020-9_bib108","doi-asserted-by":"crossref","first-page":"75","DOI":"10.1023\/A:1008236911603","article-title":"A Constraint Satisfaction Approach to a Circuit Design Problem","volume":"13","author":"Puget","year":"1998","journal-title":"Journal of Global Optimization"},{"issue":"1","key":"10.1016\/S1574-6526(06)80020-9_bib109","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1023\/A:1014785518570","article-title":"Approximate Quantified Constraint Solving by Cylindrical Box Decomposition","volume":"8","author":"Ratschan","year":"2002","journal-title":"Reliable Computing"},{"issue":"3","key":"10.1016\/S1574-6526(06)80020-9_bib110","doi-asserted-by":"crossref","first-page":"333","DOI":"10.1137\/0717027","article-title":"About the Centered Form","volume":"17","author":"Ratschek","year":"1980","journal-title":"SIAM Journal of Numerical Analysis"},{"key":"10.1016\/S1574-6526(06)80020-9_bib111","doi-asserted-by":"crossref","first-page":"514","DOI":"10.2307\/2271358","article-title":"Some Unsolvable Problems Involving Elementary Functions of a Real Variable","volume":"33","author":"Richardson","year":"1968","journal-title":"Journal of Symbolic Logic"},{"key":"10.1016\/S1574-6526(06)80020-9_bib112","doi-asserted-by":"crossref","first-page":"365","DOI":"10.1007\/BF02307386","article-title":"Enclosing Solutions of Linear Interval Equations is NP-hard","volume":"53","author":"Rohn","year":"1994","journal-title":"Computing"},{"key":"10.1016\/S1574-6526(06)80020-9_bib113","series-title":"Linear Algebra in Self-Validating Methods, volume 324 of Linear Algebra and its Applications","year":"2001"},{"key":"10.1016\/S1574-6526(06)80020-9_bib114","first-page":"77","article-title":"Developments in Reliable Computing, chapter INTLAB \u2013 IN-Terval LABoratory","author":"Rump","year":"1999"},{"issue":"2","key":"10.1016\/S1574-6526(06)80020-9_bib115","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1007\/BF00138693","article-title":"BARON: A General Purpose Global Optimization Software Package","volume":"8","author":"Sahinidis","year":"1996","journal-title":"Journal of Global Optimization"},{"key":"10.1016\/S1574-6526(06)80020-9_bib116","article-title":"An extended interval inclusion test for proving first order logic formulas over the reals","author":"Sainz","year":"2005","journal-title":"Technical report, Universitat de Girona"},{"key":"10.1016\/S1574-6526(06)80020-9_bib117","doi-asserted-by":"crossref","first-page":"85","DOI":"10.1007\/BF00143879","article-title":"Consistency Techniques for Continuous Constraints","volume":"1","author":"Sam-Haroud","year":"1996","journal-title":"Constraints"},{"key":"10.1016\/S1574-6526(06)80020-9_bib118","series-title":"A Reformulation-Linearization Technique for Solving Discrete and Continuous Nonconvex Problems","author":"Sherali","year":"1999"},{"key":"10.1016\/S1574-6526(06)80020-9_bib119","series-title":"Introduction to Numerical Analysis","author":"Stoer","year":"1991"},{"key":"10.1016\/S1574-6526(06)80020-9_bib120","series-title":"A decision method for elementary algebra and geometry","author":"Tarski","year":"1951"},{"issue":"3","key":"10.1016\/S1574-6526(06)80020-9_bib121","doi-asserted-by":"crossref","first-page":"563","DOI":"10.1007\/s10107-003-0467-6","article-title":"Global Optimization of Mixed-Integer NonLinear Programs: A Theoretical and Computational Study","volume":"99","author":"Tawarmalani","year":"2004","journal-title":"Mathematical Programming A"},{"key":"10.1016\/S1574-6526(06)80020-9_bib122","series-title":"Proceedings of International Conference on Tools with Artificial Intelligence","first-page":"157","article-title":"Subdefinite Models as a Variety of Constraint Programming","author":"Telerman","year":"1996"},{"key":"10.1016\/S1574-6526(06)80020-9_bib123","article-title":"Constraint Satisfaction in Logic Programming","author":"Van Hentenryck","year":"1989"},{"issue":"2","key":"10.1016\/S1574-6526(06)80020-9_bib124","doi-asserted-by":"crossref","first-page":"797","DOI":"10.1137\/S0036142995281504","article-title":"Solving Polynomial Systems Using a Branch and Prune Approach","volume":"34","author":"Van Hentenryck","year":"1997","journal-title":"SIAM Journal of Numerical Analysis"},{"key":"10.1016\/S1574-6526(06)80020-9_bib125","series-title":"Numerica: a Modeling Language for Global Optimization","author":"Van Hentenryck","year":"1997"},{"issue":"5","key":"10.1016\/S1574-6526(06)80020-9_bib126","doi-asserted-by":"crossref","first-page":"369","DOI":"10.1007\/s11155-005-0044-1","article-title":"Quantified Set Inversion Algorithm with Applications to Control","volume":"11","author":"Herrero Vinas","year":"2005","journal-title":"Reliable Computing"},{"key":"10.1016\/S1574-6526(06)80020-9_bib127","series-title":"Proceedings of International Symposium on Abstraction, Reformulation and Approximation, volume 2371 of Lecture Notes in Computer Science","first-page":"224","article-title":"Approximation Techniques for Nonlinear Problems with Continuum of Solutions","author":"Vu","year":"2002"},{"issue":"1","key":"10.1016\/S1574-6526(06)80020-9_bib128","first-page":"159","article-title":"ECLiPSe: A Platform for Constraint Logic Programming","volume":"12","author":"Wallace","year":"1997","journal-title":"ICL Systems Journal"},{"key":"10.1016\/S1574-6526(06)80020-9_bib129","series-title":"The Psychology of Computer Vision","article-title":"Generating Semantic Descriptions from Drawings of Scenes with Shadows","author":"Waltz","year":"1975"},{"key":"10.1016\/S1574-6526(06)80020-9_bib130","series-title":"Proceedings of World Multi-Conference on Systemics, Cybernetics and Informatics","article-title":"Constraint Explorer: a Modelling and Sizing Tool for Engineering Design","author":"Zimmer","year":"2004"}],"container-title":["Foundations of Artificial Intelligence","Handbook of Constraint Programming"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S1574652606800209?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S1574652606800209?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2025,10,28]],"date-time":"2025-10-28T02:53:34Z","timestamp":1761620014000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S1574652606800209"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006]]},"ISBN":["9780444527264"],"references-count":130,"URL":"https:\/\/doi.org\/10.1016\/s1574-6526(06)80020-9","relation":{},"ISSN":["1574-6526"],"issn-type":[{"value":"1574-6526","type":"print"}],"subject":[],"published":{"date-parts":[[2006]]}}}