{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,18]],"date-time":"2026-03-18T01:55:09Z","timestamp":1773798909362,"version":"3.50.1"},"reference-count":27,"publisher":"Elsevier BV","issue":"13","license":[{"start":{"date-parts":[[2004,11,1]],"date-time":"2004-11-01T00:00:00Z","timestamp":1099267200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computers & Operations Research"],"published-print":{"date-parts":[[2004,11]]},"DOI":"10.1016\/s0305-0548(03)00176-x","type":"journal-article","created":{"date-parts":[[2003,6,20]],"date-time":"2003-06-20T22:47:16Z","timestamp":1056149236000},"page":"2249-2262","source":"Crossref","is-referenced-by-count":17,"title":["An entropic regularization approach for mathematical programs with equilibrium constraints"],"prefix":"10.1016","volume":"31","author":[{"given":"\u015e.\u0130lker","family":"B\u0131rb\u0131l","sequence":"first","affiliation":[]},{"given":"Shu-Cherng","family":"Fang","sequence":"additional","affiliation":[]},{"given":"Jiye","family":"Han","sequence":"additional","affiliation":[]}],"member":"78","reference":[{"key":"10.1016\/S0305-0548(03)00176-X_BIB1","series-title":"Mathematical Programs with Equilibrium Constraints","author":"Luo","year":"1997"},{"key":"10.1016\/S0305-0548(03)00176-X_BIB2","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1016\/0167-6377(88)90066-1","article-title":"On the existence of optimal solutions to mathematical program with equilibrium constraints","volume":"7","author":"Harker","year":"1988","journal-title":"Operations Research Letters"},{"key":"10.1016\/S0305-0548(03)00176-X_BIB3","doi-asserted-by":"crossref","unstructured":"Ishizuka Y, Aiyoshi E. Double penalty method for bilevel optimization problems. In: Anandalingam G., Friesz TL, editors. Hierarchical Optimization, Annals of Operations Research, vol. 34. Basel: Baltzer Science Publishers, 1992. p. 73\u201388.","DOI":"10.1007\/BF02098173"},{"key":"10.1016\/S0305-0548(03)00176-X_BIB4","unstructured":"Ishizuka Y, Aiyoshi E. Regularizations for two-level optimization problems. In: Advances in optimization. Berlin: Springer, 1992. p. 239\u201355."},{"key":"10.1016\/S0305-0548(03)00176-X_BIB5","doi-asserted-by":"crossref","first-page":"254","DOI":"10.1287\/trsc.21.4.254","article-title":"Equilibrium decomposed optimization","volume":"21","author":"Suwansirikul","year":"1987","journal-title":"Transportation Science"},{"key":"10.1016\/S0305-0548(03)00176-X_BIB6","doi-asserted-by":"crossref","first-page":"18","DOI":"10.1287\/trsc.26.1.18","article-title":"A simulated annealing approach to the network design problem with variational inequality constraints","volume":"26","author":"Friesz","year":"1992","journal-title":"Transportation Science"},{"key":"10.1016\/S0305-0548(03)00176-X_BIB7","doi-asserted-by":"crossref","unstructured":"Kanzow C. Some noninterior continuation methods for linear complementarity problems. SIAM Journal on Matrix Analysis and Applications 1996;17:851\u201368.","DOI":"10.1137\/S0895479894273134"},{"key":"10.1016\/S0305-0548(03)00176-X_BIB8","series-title":"Ill-posed variational problems and regularization techniques","first-page":"99","article-title":"Convergence of smoothing continuation method for mathematical programs with complementarity constraints","volume":"vol. 477","author":"Fukushima","year":"2000"},{"key":"10.1016\/S0305-0548(03)00176-X_BIB9","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1007\/s101070050048","article-title":"A smoothing method for mathematical programs with equilibrium constraints","volume":"85","author":"Facchinei","year":"1999","journal-title":"Mathematical Programming"},{"key":"10.1016\/S0305-0548(03)00176-X_BIB10","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1007\/BF01582255","article-title":"Finite-dimensional and variational inequality and nonlinear complementarity problems","volume":"48","author":"Harker","year":"1990","journal-title":"Mathematical Programming"},{"key":"10.1016\/S0305-0548(03)00176-X_BIB11","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1007\/BF01585928","article-title":"On bilevel programming, part I","volume":"48","author":"Falk","year":"1995","journal-title":"Mathematical Programming"},{"key":"10.1016\/S0305-0548(03)00176-X_BIB12","doi-asserted-by":"crossref","first-page":"51","DOI":"10.1007\/BF01592244","article-title":"Smoothing methods for convex inequalities and linear complementarity problems","volume":"71","author":"Chen","year":"1995","journal-title":"Mathematical Programming"},{"key":"10.1016\/S0305-0548(03)00176-X_BIB13","doi-asserted-by":"crossref","first-page":"402","DOI":"10.1137\/S036301299223619X","article-title":"A globally convergent successive approximation methods for nonsmooth equations","volume":"33","author":"Qi","year":"1995","journal-title":"SIAM Journal on Control and Optimization"},{"key":"10.1016\/S0305-0548(03)00176-X_BIB14","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1007\/BF01584847","article-title":"A continuation method for (strongly) monotone variational inequalities","volume":"89","author":"Kanzow","year":"1998","journal-title":"Mathematical Programming"},{"key":"10.1016\/S0305-0548(03)00176-X_BIB15","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1016\/0898-1221(96)00145-9","article-title":"Solving min-max problems and linear semi-infinite programs","volume":"32","author":"Fang","year":"1996","journal-title":"Computers and Mathematics with Applications"},{"key":"10.1016\/S0305-0548(03)00176-X_BIB16","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1007\/BF01199466","article-title":"On the entropic regularization method for solving min-max problems with applications","volume":"46","author":"Li","year":"1997","journal-title":"Mathematical Methods of Operations Research"},{"key":"10.1016\/S0305-0548(03)00176-X_BIB17","series-title":"Entropy optimization and mathematical programming","author":"Fang","year":"1997"},{"key":"10.1016\/S0305-0548(03)00176-X_BIB18","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1016\/S0021-9800(70)80010-2","article-title":"A generalization of the linear complementarity problem","volume":"8","author":"Cottle","year":"1970","journal-title":"Journal of Combinatorial Theory"},{"key":"10.1016\/S0305-0548(03)00176-X_BIB19","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1287\/moor.25.1.1.15213","article-title":"Mathematical programs with complementarity constraints","volume":"25","author":"Scheel","year":"2000","journal-title":"Mathematics of Operations Research"},{"key":"10.1016\/S0305-0548(03)00176-X_BIB20","series-title":"Analytic inequalities","author":"Kazarinoff","year":"1961"},{"key":"10.1016\/S0305-0548(03)00176-X_BIB21","unstructured":"Gill PE, Murray W, Saunders MA, Drud A, Kalvelagen E. GAMS\/SNOPT: an SQP algorithm for large-scale constrained optimization, 2000. http:\/\/www.gams.com\/docs\/solver\/snopt.pdf."},{"key":"10.1016\/S0305-0548(03)00176-X_BIB22","series-title":"Iterative solution of nonlinear equations in several variables","author":"Ortega","year":"1980"},{"key":"10.1016\/S0305-0548(03)00176-X_BIB23","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1016\/0377-2217(91)90325-P","article-title":"Generalized Nash games and quasi-variational inequalities","volume":"54","author":"Harker","year":"1991","journal-title":"European Journal of Operational Research"},{"key":"10.1016\/S0305-0548(03)00176-X_BIB24","doi-asserted-by":"crossref","unstructured":"Dolan ED, Munson TS. The Kestrel interface to the NEOS server, 2001. http:\/\/www-neos.mcs.anl.gov\/neos\/ftp\/kestrel.ps.","DOI":"10.2172\/786920"},{"key":"10.1016\/S0305-0548(03)00176-X_BIB25","unstructured":"AMPL. AMPL home page, 2002. http:\/\/www.ampl.com."},{"key":"10.1016\/S0305-0548(03)00176-X_BIB26","doi-asserted-by":"crossref","first-page":"105","DOI":"10.1007\/BF01585759","article-title":"A numerical approach to optimization problems with variational inequality constraints","volume":"68","author":"Outrata","year":"1995","journal-title":"Mathematical Programming"},{"key":"10.1016\/S0305-0548(03)00176-X_BIB27","doi-asserted-by":"crossref","first-page":"265","DOI":"10.1007\/BF01582259","article-title":"Sensitivity analysis based heuristic algorithms for mathematical programs with variational inequalities","volume":"48","author":"Riesz","year":"1990","journal-title":"Mathematical Programming"}],"container-title":["Computers & Operations Research"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S030505480300176X?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S030505480300176X?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2019,3,20]],"date-time":"2019-03-20T07:53:59Z","timestamp":1553068439000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S030505480300176X"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2004,11]]},"references-count":27,"journal-issue":{"issue":"13","published-print":{"date-parts":[[2004,11]]}},"alternative-id":["S030505480300176X"],"URL":"https:\/\/doi.org\/10.1016\/s0305-0548(03)00176-x","relation":{},"ISSN":["0305-0548"],"issn-type":[{"value":"0305-0548","type":"print"}],"subject":[],"published":{"date-parts":[[2004,11]]}}}