Optimality Conditions for Disjunctive Optimization in Reflexive Banach Spaces

被引：0
作者：
Wen Song
Qianqian Wang
机构：
[1] School of Mathematical Sciences,
[2] Harbin Normal University,undefined
来源：
Journal of Optimization Theory and Applications | 2015年 / 164卷
关键词：
Reflexive Banach space; Disjunctive optimization; Convex generalized polyhedron; Mordukhovich normal cone; Optimality condition; 90C30; 90C46;
D O I：
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学科分类号：
摘要：
We study optimization problems with the constraints having disjunctive structures in reflexive Banach spaces. By the representations of contingent cones and Fréchet normal cones to finite unions of sets in general Banach spaces and using the special structures of convex generalized polyhedral sets, we calculate the Mordukhovich normal cones to finite unions of closed and convex sets that particularly include convex generalized polyhedral sets in reflexive Banach spaces. Furthermore, based on these calculations and the Guignard-type constraint qualifications, we derive new optimality conditions for disjunctive optimization problems. We also present specializations of these results to optimization problems with variational inequality constraints.
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页码：436 / 454
页数：18
相关论文
共 35 条
[1]  
Balas E(1977)A note on duality in disjunctive programming J. Optim. Theory Appl. 21 523-528
[2]  
Glover F(1975)Polyhedral annexation in mixed integer and combinatorial programming Math. Program. 8 161-188
[3]  
Jeroslow RG(1977)Representability in mixed integer programming i: characterization results Appl. Math. 17 223-243
[4]  
Borwein JM(1980)A strong duality theorem for the minimum of a family of convex programs J. Optim. Theory Appl. 31 453-472
[5]  
Helbig S(1994)Duality in disjunctive programming via vector optimization Math. Program. 65 21-41
[6]  
Gugat M(1997)Parametric disjunctive programming: one-sided differentiability of the value function J. Optim. Theory Appl. 92 285-310
[7]  
Ceria S(1999)Convex programming for disjunctive convex optimization Math. Program. 86 596-614
[8]  
Soares J(2008)Quasiconvex minimization on a locally finite union of convex sets J. Optim. Theory Appl. 139 1-16
[9]  
Aussel D(2007)Optimality conditions for disjunctive programs with application to mathematical programs with equilibrium constraints Set-Valued Anal. 15 139-162
[10]  
Ye JJ(2008)On calculating the normal cone to a finite union of convex polyhedra Optimization 57 57-78
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