{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T17:29:33Z","timestamp":1787333373367,"version":"build-2736575974"},"reference-count":23,"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":[[1998,11]]},"abstract":"<jats:p>\n                    We consider the problem of minimizing a real-valued function f\n                    <jats:sup>0<\/jats:sup>\n                    (x)subject to max-min constraints, i.e., constraints of the form ${\\rm max}_{k\\in{\\bf r}}{\\rm min}_{j\\in{\\bf q}_k} f_k^j(x) \\le 0$, where for any integer r, ${\\bf r} \\mathrel{\\buildrel\\Delta\\over={1,,...,r}, so that for any k \\in {\\bf r,\\, q}_k ={1,...,q\n                    <jats:sub>k<\/jats:sub>\n                    }. Problems with this kind of constraint arise in a variety of applications, such as design of electronic circuits subject to manufacturing tolerances and postmanufacturing tuning and optimal steering of mobile robots in the presence of obstacles.\n                  <\/jats:p>\n                  <jats:p>An optimization problem with max-min constraints is equivalent to a collection of optimization problems with smooth inequality constraints. This collection can be very large, and hence solving an optimization problem with max-min constraints by solving each member of the collection can be exorbitantly expensive. We present a transcription of problems of this type into a single inequality constrained nonlinear programming problem with smooth constraints, which can be solved using readily available software. The transcription is based on the fact that a set of real numbers contains a nonpositive element if and only if its convex hull contains a nonpositive element. While this fact is fairly obvious, establishing a correspondence between the global and local minimizers of the original problem and those of the problem resulting from our transcription turned out to be quite difficult.<\/jats:p>\n                  <jats:p>The significant advantages of using our transcription are demonstrated by the numerical examples that are included in the paper to illustrate the effectiveness of our approach.<\/jats:p>","DOI":"10.1137\/s1052623496298534","type":"journal-article","created":{"date-parts":[[2003,6,11]],"date-time":"2003-06-11T11:12:06Z","timestamp":1055329926000},"page":"887-915","source":"Crossref","is-referenced-by-count":30,"title":["On the Conversion of Optimization Problems with Max-Min Constraints to Standard Optimization Problems"],"prefix":"10.1137","volume":"8","author":[{"given":"C.","family":"Kirjner-Neto","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"E.","family":"Polak","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":"10.1109\/TCS.1976.1084191"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1287\/opre.22.5.1086"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1109\/43.125095"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1109\/JRA.1985.1087003"},{"key":"R5","doi-asserted-by":"crossref","unstructured":"P. E. Gill, W. Murray, M. A. Saunders, and M. H. Wright,\n                      User\u2019s Guide for NPSOL: A Fortran Package for Nonlinear Programming\n                      , Technical Report 86\u20102, Dept. of Operations Research, Stanford University, Stanford, CA, 1986.","DOI":"10.21236\/ADA169115"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1002\/aic.690240612"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1002\/aic.690290312"},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1109\/9.50336"},{"key":"R9","unstructured":"D. Hochbaum,\n                      Complexity and algorithms for logical constraints with applications to VLSI layout, compaction and clocking\n                      , Studies in Locational Analysis, ISOLD VI Proceedings, 1993, pp. 159\u2013164."},{"key":"R10","doi-asserted-by":"publisher","DOI":"10.1016\/0098-1354(94)85007-0"},{"key":"R11","doi-asserted-by":"publisher","DOI":"10.1137\/S0363012994266188"},{"key":"R12","doi-asserted-by":"crossref","unstructured":"P. C. Liu, V. W. Chung, and K. C. Li,\n                      Circuit design with post\u2010fabrication tuning\n                      , in Proc. 35th Midwest Symposium on Circuits and Systems, Washington, DC, IEEE, NY, 1992, pp. 344\u2013347.","DOI":"10.1109\/MWSCAS.1992.271290"},{"key":"R13","doi-asserted-by":"publisher","DOI":"10.1007\/BF00940285"},{"key":"R14","doi-asserted-by":"publisher","DOI":"10.1007\/BF00934131"},{"key":"R15","doi-asserted-by":"publisher","DOI":"10.1145\/355934.355936"},{"key":"R16","unstructured":"G. Muller,\n                      On computer\u2010aided tuning of microwave filters\n                      , in IEEE Proc. International Symposium on Circuits and Systems, Munich, IEEE Computer Society Press, Los Alamitos, CA, 1976, pp. 722\u2013725."},{"key":"R17","doi-asserted-by":"publisher","DOI":"10.1016\/0098-1354(93)E0013-Y"},{"key":"R18","doi-asserted-by":"publisher","DOI":"10.1109\/TCS.1979.1084702"},{"key":"R19","doi-asserted-by":"publisher","DOI":"10.1007\/BF00934703"},{"key":"R20","doi-asserted-by":"publisher","DOI":"10.1007\/BF01585175"},{"key":"R21","unstructured":"E. Polak,\n                      Optimization: Algorithms and Consistent Approximations\n                      , Springer\u2010Verlag, New York, 1997."},{"key":"R22","doi-asserted-by":"publisher","DOI":"10.2140\/pjm.1990.145.367"},{"key":"R23","doi-asserted-by":"publisher","DOI":"10.1007\/BF00938449"}],"container-title":["SIAM Journal on Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/S1052623496298534","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T16:54:31Z","timestamp":1787331271000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/S1052623496298534"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1998,11]]},"references-count":23,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1998,11]]}},"alternative-id":["10.1137\/S1052623496298534"],"URL":"https:\/\/doi.org\/10.1137\/s1052623496298534","relation":{},"ISSN":["1052-6234","1095-7189"],"issn-type":[{"value":"1052-6234","type":"print"},{"value":"1095-7189","type":"electronic"}],"subject":[],"published":{"date-parts":[[1998,11]]}}}