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http://dx.doi.org/10.14403/jcms.2014.27.3.433

ON SURROGATE DUALITY FOR ROBUST SEMI-INFINITE OPTIMIZATION PROBLEM  

Lee, Gue Myung (Department of Applied Mathematics Pukyong National University)
Lee, Jae Hyoung (Department of Applied Mathematics Pukyong National University)
Publication Information
Journal of the Chungcheong Mathematical Society / v.27, no.3, 2014 , pp. 433-438 More about this Journal
Abstract
A semi-infinite optimization problem involving a quasi-convex objective function and infinitely many convex constraint functions with data uncertainty is considered. A surrogate duality theorem for the semi-infinite optimization problem is given under a closed and convex cone constraint qualification.
Keywords
quasi-convex objective function; surrogate duality; semi-infinite optimization problem with data uncertainty; constraint qualification;
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1 D. G. Luenberger, Quasi-convex programming, SIAM J. Appl. Math. 16 (1968), 1090-1095.   DOI   ScienceOn
2 V. Jeyakumar, G. M. Lee, and N. Dinh, New sequential Lagrange multiplier conditions characterizing optimality without constraint qualification for convex programs, SIAM J. Optim. 20 (2003), 534-547.
3 V. Jeyakumar and G. Y. Li, Strong duality in robust convex programming:complete characterizations, SIAM J. Optim. 20 (2010), 3384-3407.   DOI   ScienceOn
4 G. Y. Li, V. Jeyakumar, and G. M. Lee, Robust conjugate duality for convex op-timization under uncertainty with application to data classification, Nonlinear Anal. 74 (2011), 2327-2341.   DOI   ScienceOn
5 J. P. Penot and M. Volle, On quasi-convex duality, Math. Oper. Res. 15 (1990), 597-625.   DOI
6 J. P. Penot and M. Volle, Surrogate programming and multipliers in quasi-convex programming, SIAM J. Control Optim. 42 (2004), 1994-2003.   DOI   ScienceOn
7 S. Suzuki and D. Kuroiwa, Necessary and sufficient constraint qualification for surrogate duality, J. Optim. Theory Appl. 152 (2012), 366-377.   DOI
8 S. Suzuki, D. Kuroiwa, and G. M. Lee, Surrogate duality for robust optimiza-tion, European J. Oper. Res. 231 (2013), 257-262.   DOI   ScienceOn
9 H. J. Greenberg and W. P. Pierskalla, Surrogate mathematical programming, Oper. Res. 18 (1970), 924-939.   DOI   ScienceOn
10 A. Beck and A. Ben-Tal, Duality in robust optimization: primal worst equals dual best, Oper. Res. Lett. 37 (2009), 1-6.   DOI   ScienceOn
11 H. J. Greenberg, Quasi-conjugate functions and surrogate duality, Oper. Res. 21 (1973), 162-178.   DOI   ScienceOn
12 F. Glover, A Multiphase-dual algorithm for the zero-one integer programming problem, Oper. Res. 13 (1965), 879-919.   DOI   ScienceOn