{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T16:57:35Z","timestamp":1760029055216},"reference-count":44,"publisher":"University of Zielona G\u00f3ra, Poland","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2012,6,1]]},"abstract":"<jats:title>A modified filter SQP method as a tool for optimal control of nonlinear systems with spatio-temporal dynamics<\/jats:title><jats:p>Our aim is to adapt Fletcher's filter approach to solve optimal control problems for systems described by nonlinear Partial Differential Equations (PDEs) with state constraints. To this end, we propose a number of modifications of the filter approach, which are well suited for our purposes. Then, we discuss possible ways of cooperation between the filter method and a PDE solver, and one of them is selected and tested.<\/jats:p>","DOI":"10.2478\/v10006-012-0023-8","type":"journal-article","created":{"date-parts":[[2012,6,29]],"date-time":"2012-06-29T14:49:17Z","timestamp":1340981357000},"page":"313-326","source":"Crossref","is-referenced-by-count":6,"title":["A modified filter SQP method as a tool for optimal control of nonlinear systems with spatio-temporal dynamics"],"prefix":"10.61822","volume":"22","author":[{"given":"Ewaryst","family":"Rafaj\u0142owicz","sequence":"first","affiliation":[]},{"given":"Krystyn","family":"Stycze\u0144","sequence":"additional","affiliation":[]},{"given":"Wojciech","family":"Rafaj\u0142owicz","sequence":"additional","affiliation":[]}],"member":"37438","reference":[{"key":"1","doi-asserted-by":"crossref","first-page":"5083","DOI":"10.1016\/S0009-2509(02)00419-0","article-title":"Dynamic optimization of dissipative PDE systems using nonlinear order reduction","volume":"57","author":"A. Armaou","year":"2002","journal-title":"Chemical Engineering Science"},{"issue":"3","key":"2","doi-asserted-by":"crossref","first-page":"380","DOI":"10.1134\/S106423071003007X","article-title":"Approaches to control design and optimization in heat transfer problems","volume":"49","author":"H. Aschemanna","year":"2010","journal-title":"International Journal of Computer and Systems Sciences"},{"issue":"4","key":"3","doi-asserted-by":"crossref","first-page":"980","DOI":"10.1137\/S105262340138983X","article-title":"A pattern search filter method for nonlinear programming without derivatives","volume":"14","author":"C. Audet","year":"2004","journal-title":"SIAM Journal on Optimization"},{"issue":"1","key":"4","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1023\/B:COAP.0000018878.95983.4e","article-title":"STRSCNE: A scaled trust-region solver for constrained nonlinear equations","volume":"28","author":"S. Bellavia","year":"2004","journal-title":"Computational Optimization and Applications"},{"key":"5","doi-asserted-by":"crossref","DOI":"10.1137\/1.9780898718577","volume-title":"Practical Methods for Optimal Control and Estimation Using Nonlinear Programming","author":"J. Betts","year":"2010"},{"key":"6","doi-asserted-by":"crossref","DOI":"10.1137\/1.9780898719383","volume-title":"Nonlinear Programming. Concepts, Algorithms, and Applications to Chemical Processes","author":"L. Biegler","year":"2010"},{"issue":"1","key":"7","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1007\/BF00939935","article-title":"Functional and numerical solution of a control problem originating from heat transfer","volume":"68","author":"J. Burger","year":"1991","journal-title":"Journal of Optimization Theory and Applications"},{"key":"8","doi-asserted-by":"crossref","first-page":"76","DOI":"10.1093\/imamat\/6.1.76","article-title":"The convergence of a class of double-rank minimization algorithms","volume":"6","author":"C. Broyden","year":"1970","journal-title":"Journal of the Institute of Mathematics and Its Applications"},{"key":"9","volume-title":"Distributed Control Systems","author":"A. Butkovskiy","year":"1969"},{"issue":"5","key":"10","doi-asserted-by":"crossref","first-page":"2281","DOI":"10.1137\/080738222","article-title":"Infeasibility detection and SQPmethods for nonlinear optimization","volume":"20","author":"R. Byrd","year":"2010","journal-title":"SIAM Journal on Optimization"},{"issue":"1","key":"11","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1007\/s10107-003-0378-6","article-title":"On the global convergence of an SLP-filter algorithm that takes EQP steps","volume":"96","author":"C. Chin","year":"2003","journal-title":"Mathematical Programming"},{"issue":"3","key":"12","doi-asserted-by":"crossref","first-page":"365","DOI":"10.1080\/10556780600565489","article-title":"Global and local convergence of a filter line search method for non-linear programming","volume":"22","author":"C. Chin","year":"2007","journal-title":"Optimization Methods and Software"},{"key":"13","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-0185-4","volume-title":"Nonlinear and Robust Control of PDE Systems: Methods and Applications to Transport-Reaction Processes","author":"P. Christofides","year":"2001"},{"key":"14","doi-asserted-by":"crossref","DOI":"10.1137\/1.9780898719857","volume-title":"Trust-Region Methods","author":"A. Conn","year":"2000"},{"issue":"3","key":"15","doi-asserted-by":"crossref","first-page":"415","DOI":"10.1016\/j.automatica.2003.10.023","article-title":"A new actuator activation policy for performance enhancement of controlled diffusion processes","volume":"40","author":"M. Demetriou","year":"2004","journal-title":"Automatica"},{"issue":"3","key":"16","doi-asserted-by":"crossref","first-page":"715","DOI":"10.1016\/S0005-1098(02)00304-7","article-title":"Analysis and control of parabolic PDE systems with input constraints","volume":"39","author":"N. El-Farra","year":"2003","journal-title":"Automatica"},{"key":"17","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511574795","volume-title":"Infinite Dimensional Optimization and Control Theory","author":"H. Fattorini","year":"1999"},{"issue":"2","key":"18","doi-asserted-by":"crossref","first-page":"239","DOI":"10.1007\/s101070100244","article-title":"Nonlinear programming without a penalty function","volume":"91","author":"R. Fletcher","year":"2002","journal-title":"Mathematical Programming, Series A"},{"issue":"1","key":"19","doi-asserted-by":"crossref","first-page":"44","DOI":"10.1137\/S105262340038081X","article-title":"On the global convergence of a filter-SQP algorithm","volume":"13","author":"R. Fletcher","year":"2002a","journal-title":"SIAM Journal on Optimization"},{"issue":"3","key":"20","doi-asserted-by":"crossref","first-page":"635","DOI":"10.1137\/S1052623499357258","article-title":"Global convergence of trust-region SQP-filter algorithms for general nonlinear programming","volume":"13","author":"R. Fletcher","year":"2002b","journal-title":"SIAM Journal on Optimization"},{"key":"21","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-11339-0_3","volume-title":"Nonlinear Optimization","volume":"1989","author":"R. Fletcher","year":"2010"},{"issue":"5","key":"22","doi-asserted-by":"crossref","first-page":"935","DOI":"10.1007\/s00158-009-0450-9","article-title":"An SLP Filter algorithm for probabilistic analytical target cascading","volume":"41","author":"J. Han","year":"2010","journal-title":"Structural and Multidisciplinary Optimization"},{"key":"23","volume-title":"Optimization with PDE Constraints","author":"M. Hinze","year":"2009"},{"key":"24","volume-title":"Control Theory for Partial Differential Equations: Continuous and Approximation Theories, Vol. I: Abstract Parabolic Systems, Vol. II: Abstract Hyperbolic-Like Systems over a Finite Time Horizon","volume":"74","author":"I. Lasiecka","year":"2000"},{"key":"25","volume-title":"Von Karman Evolution Equations: Well-posedness and Long Time Dynamics","author":"I. Lasiecka","year":"2010"},{"key":"26","volume-title":"Long-time Behavior of Second Order Evolution Equations with Nonlinear Damping","author":"I. Lasiecka","year":"2008"},{"issue":"5","key":"27","first-page":"609","article-title":"A new SQP-filter method for solving nonlinear programming problems","volume":"24","author":"D. Li","year":"2006","journal-title":"Journal of Computational Mathematics"},{"issue":"2","key":"28","doi-asserted-by":"crossref","first-page":"1000","DOI":"10.1016\/j.amc.2005.03.004","article-title":"A trust-region filter method for general non-linear programming","volume":"172","author":"P. Nie","year":"2006","journal-title":"Applied Mathematics and Computation"},{"key":"29","volume-title":"Optimal Control of Nonlinear Parabolic Systems","author":"P. Nettaanmaki","year":"1994"},{"key":"30","volume-title":"Numerical Optimization","author":"J. Nocedal","year":"2006"},{"issue":"7","key":"31","doi-asserted-by":"crossref","first-page":"629","DOI":"10.1109\/34.56205","article-title":"Scale-space and edge detection using anisotropic diffusion","volume":"12","author":"P. Perona","year":"1990","journal-title":"IEEE Transactions on Pattern Analysis and Machine Intelligence"},{"key":"32","doi-asserted-by":"crossref","first-page":"314","DOI":"10.1109\/TCST.2007.903398","article-title":"Testing homogeneity of coefficients in distributed systems with application to quality monitoring","volume":"16","author":"E. Rafaj\u0142owicz","year":"2008","journal-title":"IEEE Transactions on Control Systems Technology"},{"issue":"2","key":"33","doi-asserted-by":"crossref","first-page":"453","DOI":"10.1002\/asjc.172","article-title":"Testing (non-)linearity of distributed-parameter systems from a video sequence","volume":"12","author":"E. Rafaj\u0142owicz","year":"2010","journal-title":"Asian Journal of Control"},{"key":"34","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4419-5762-7","volume-title":"Numerical Data Fitting in Dynamical Systems; A Practical Introduction with Applications and Software","volume":"77","author":"K. Schittkowski","year":"2002"},{"issue":"12","key":"35","doi-asserted-by":"crossref","first-page":"2999","DOI":"10.1016\/j.apnum.2009.07.009","article-title":"An active set strategy for solving optimization problems with up to 200,000,000 nonlinear constraints","volume":"59","author":"K. Schittkowski","year":"2009","journal-title":"Applied Numerical Mathematics"},{"issue":"2","key":"36","doi-asserted-by":"crossref","first-page":"235","DOI":"10.1016\/j.apnum.2008.01.005","article-title":"Global convergence of a tridimensional filter SQP algorithm based on the line search method","volume":"59","author":"C. Shen","year":"2009","journal-title":"Applied Numerical Mathematics"},{"issue":"1","key":"37","doi-asserted-by":"crossref","first-page":"34","DOI":"10.1016\/j.ejor.2010.02.031","article-title":"Global convergence of a robust filter SQP algorithm","volume":"206","author":"C. Shen","year":"2010","journal-title":"European Journal of Operational Research"},{"key":"38","doi-asserted-by":"publisher","DOI":"10.1155\/2009\/137483","article-title":"Evolutionary search for globally optimal stable multicycles in complex systems with inventory couplings","author":"M. Skowron","year":"2009","journal-title":"International Journal of Chemical Engineering"},{"issue":"1","key":"39","doi-asserted-by":"crossref","first-page":"92","DOI":"10.1016\/j.amc.2007.04.014","article-title":"A modified SQP-filter method and its global convergence","volume":"194","author":"K. Su","year":"2007","journal-title":"Applied Mathematics and Computation"},{"issue":"2","key":"40","doi-asserted-by":"crossref","first-page":"240","DOI":"10.1016\/j.camwa.2008.05.030","article-title":"A modified SQP method with non-monotone technique and its global convergence","volume":"57","author":"K. Su","year":"2009","journal-title":"Computers and Mathematics with Applications"},{"key":"41","doi-asserted-by":"crossref","DOI":"10.1090\/gsm\/112","volume-title":"Optimal Control of Partial Differential Equations. Theory, Methods and Applications","author":"F. Troltzsch","year":"2010"},{"key":"42","doi-asserted-by":"crossref","first-page":"68","DOI":"10.1007\/978-3-642-13800-3_6","volume-title":"Learning and Intelligent Optimization","volume":"6073","author":"A. Turco","year":"2010"},{"key":"43","volume-title":"Optimal Measurement Methods for Distributed Parameter System Identification","author":"D. Uci\u0144ski","year":"2005"},{"issue":"1","key":"44","doi-asserted-by":"crossref","first-page":"217","DOI":"10.1007\/s10107-003-0491-6","article-title":"On the superlinear local convergence of a filter-SQP method","volume":"100","author":"S. Ulbrich","year":"2004","journal-title":"Mathematical Programming, Series B"}],"container-title":["International Journal of Applied Mathematics and Computer Science"],"original-title":[],"link":[{"URL":"http:\/\/content.sciendo.com\/view\/journals\/amcs\/22\/2\/article-p313.xml","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/view\/j\/amcs.2012.22.issue-2\/v10006-012-0023-8\/v10006-012-0023-8.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,2,29]],"date-time":"2024-02-29T10:27:28Z","timestamp":1709202448000},"score":1,"resource":{"primary":{"URL":"https:\/\/content.sciendo.com\/doi\/10.2478\/v10006-012-0023-8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,6,1]]},"references-count":44,"journal-issue":{"issue":"2"},"URL":"https:\/\/doi.org\/10.2478\/v10006-012-0023-8","relation":{},"ISSN":["1641-876X"],"issn-type":[{"value":"1641-876X","type":"print"}],"subject":[],"published":{"date-parts":[[2012,6,1]]}}}