{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,22]],"date-time":"2026-08-22T09:01:51Z","timestamp":1787389311670,"version":"build-2736575974"},"reference-count":40,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Optim."],"published-print":{"date-parts":[[1999,1]]},"abstract":"<jats:p>Diverse problems in optimization, engineering, and economics have natural formulations in terms of complementarity conditions, which state (in their simplest form) that either a certain nonnegative variable must be zero or a corresponding inequality must hold with equality, or both. A variety of algorithms has been devised for solving problems expressed in terms of complementarity conditions. It is thus attractive to consider extending algebraic modeling languages, which are widely used for sending ordinary equations and inequality constraints to solvers, so that they can express complementarity problems directly. We describe an extension to the AMPL modeling language that can express the most common complementarity conditions in a concise and flexible way, through the introduction of a single new \"complements\" operator. We present details of an efficient implementation that incorporates an augmented presolve phase to simplify complementarity problems, and that converts complementarity conditions to a canonical form convenient for solvers.<\/jats:p>","DOI":"10.1137\/s105262349833338x","type":"journal-article","created":{"date-parts":[[2003,6,11]],"date-time":"2003-06-11T11:12:06Z","timestamp":1055329926000},"page":"991-1009","source":"Crossref","is-referenced-by-count":21,"title":["Expressing Complementarity Problems in an Algebraic Modeling Language and Communicating Them to Solvers"],"prefix":"10.1137","volume":"9","author":[{"given":"Michael C.","family":"Ferris","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Robert","family":"Fourer","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"David M.","family":"Gay","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,31]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1287\/moor.8.2.260"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1002\/nav.3800310104"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1007\/BF01580720"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1023\/A:1008632215341"},{"key":"R5","unstructured":"J. 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Stone,\n                      The Linear Complementarity Problem\n                      , Academic Press, New York, 1992."},{"key":"R11","unstructured":"S. P. Dirkse,\n                      Robust Solution of Mixed Complementarity Problems\n                      , Mathematical Programming Technical Report 94\u201012, Computer Sciences Department, University of Wisconsin, Madison, 1994;"},{"key":"R11","unstructured":"also available online from ftp:\/\/ftp.cs.wisc.edu\/math\u2010prog\/tech\u2010reports\/94\u201012.ps. Z."},{"key":"R12","doi-asserted-by":"publisher","DOI":"10.1080\/10556789508805606"},{"key":"R13","doi-asserted-by":"publisher","DOI":"10.1080\/10556789508805619"},{"key":"R13","unstructured":"also available online from ftp:\/\/ftp.cs.wisc.edu\/math\u2010prog\/mcplib\/."},{"key":"R14","unstructured":"Steven Dirkse, Michael Ferris, Modeling and solution environments for MPEC: GAMS & MATLAB, Appl. Optim., Vol. 22, Kluwer Acad. Publ., Dordrecht, 1999, 127\u20131472000a:90077"},{"key":"R15","unstructured":"S. P. Dirkse, M. C. Ferris, P. V. Preckel, and T. F. Rutherford,\n                      The GAMS Callable Program Library for Variational and Complementarity Solvers\n                      , Mathematical Programming Technical Report 94\u201007, Computer Sciences Department, University of Wisconsin, Madison, 1994;"},{"key":"R15","unstructured":"also available online from ftp:\/\/ftp.cs.wisc.edu\/math\u2010prog\/tech\u2010reports\/94\u201007.ps. Z."},{"key":"R16","doi-asserted-by":"publisher","DOI":"10.1023\/A:1008636318275"},{"key":"R17","volume-title":"Complementarity and variational problems","author":"Ferris Michael","year":"1997"},{"key":"R18","doi-asserted-by":"publisher","DOI":"10.1137\/S0036144595285963"},{"key":"R19","unstructured":"Robert Fourer, Extending a general\u2010purpose algebraic modeling language to combinatorial optimization: a logic programming approach, Oper. Res.\/Comput. Sci. Interfaces Ser., Vol. 9, Kluwer Acad. Publ., Boston, MA, 1998, 31\u201374CMP1602400"},{"key":"R20","unstructured":"Robert Fourer, David Gay, Experience with a primal presolve algorithm, Kluwer Acad. Publ., Dordrecht, 1994, 135\u20131541307169"},{"key":"R21","doi-asserted-by":"publisher","DOI":"10.1287\/ijoc.7.2.166"},{"key":"R22","doi-asserted-by":"publisher","DOI":"10.1287\/mnsc.36.5.519"},{"key":"R23","unstructured":"R. Fourer, D. M. Gay, and B. W. Kernighan,\n                      AMPL: A Modeling Language for Mathematical Programming\n                      , Scientific Press\/Duxbury Press, San Francisco, CA, 1993."},{"key":"R24","unstructured":"D. M. Gay,\n                      Hooking Your Solver to AMPL\n                      , Technical Report 97\u20104\u201006, Computing Sciences Research Center, Bell Laboratories, Lucent Technologies, 1997;"},{"key":"R24","unstructured":"also available online from http:\/\/www.ampl.com\/ampl\/REFS\/hooking2.ps.gz."},{"key":"R25","unstructured":"D. C. Hanselman and B. C. Littlefield,\n                      Mastering MATLAB 5: A Comprehensive Tutorial and Reference\n                      , Prentice\u2010Hall, Upper Saddle River, NJ, 1997."},{"key":"R26","doi-asserted-by":"publisher","DOI":"10.1007\/BF01582255"},{"key":"R27","doi-asserted-by":"publisher","DOI":"10.1002\/fld.1650040407"},{"key":"R28","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-6377(99)00052-8"},{"key":"R29","doi-asserted-by":"publisher","DOI":"10.1016\/0025-5610(96)82521-4"},{"key":"R30","unstructured":"T. S. Munson,\n                      Private communication\n                      , December 1997."},{"key":"R31","unstructured":"D. Redfern and C. Campbell,\n                      MATLAB Handbook\n                      , Springer\u2010Verlag, New York, 1998."},{"key":"R32","unstructured":"R. T. Rockafellar,\n                      Convex Analysis\n                      , Princeton University Press, Princeton, NJ, 1970."},{"key":"R33","unstructured":"T. F. Rutherford,\n                      MILES: A Mixed Inequality and Nonlinear Equation Solver\n                      , Working paper, Dept. of Economics, University of Colorado, 1993;"},{"key":"R33","unstructured":"also available online from http:\/\/robles.colorado.edu\/~tomruth\/milesdoc\/milesdoc.htm."},{"key":"R34","doi-asserted-by":"publisher","DOI":"10.1016\/0165-1889(94)00831-2"},{"key":"R35","unstructured":"L. Schrage,\n                      Optimization Modeling with LINGO\n                      , LINDO Systems, Chicago, IL, 1998."}],"container-title":["SIAM Journal on Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/S105262349833338X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T16:46:45Z","timestamp":1787330805000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/S105262349833338X"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1999,1]]},"references-count":40,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1999,1]]}},"alternative-id":["10.1137\/S105262349833338X"],"URL":"https:\/\/doi.org\/10.1137\/s105262349833338x","relation":{},"ISSN":["1052-6234","1095-7189"],"issn-type":[{"value":"1052-6234","type":"print"},{"value":"1095-7189","type":"electronic"}],"subject":[],"published":{"date-parts":[[1999,1]]}}}