Optimality conditions for convex problems on intersections of non necessarily convex sets

被引：0
作者：
E. Allevi
J. E. Martínez-Legaz
R. Riccardi
机构：
[1] Università degli Studi di Brescia,Dipartimento di Economia e Management
[2] Universitat Autònoma de Barcelona,Departament d’Economia i d’Història Econòmica
[3] BGSMath,undefined
来源：
Journal of Global Optimization | 2020年 / 77卷
关键词：
Convex optimization; Nonsmooth optimization; Optimality conditions; 90C25; 90C26; 90C46;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We present necessary and sufficient optimality conditions for the minimization of pseudoconvex functions over convex intersections of non necessarily convex sets. To this aim, we use the notion of local normal cone to a closed set at a point, due to Linh and Penot (SIAM J Optim 17:500–510, 2006). The technique we use to obtain the optimality conditions is based on the so called canonical representation of a closed set by means of its associated oriented distance function.
引用
收藏
页码：143 / 155
页数：12
相关论文
共 19 条
  • [1] Dutta J(2013)Optimality conditions in convex optimization revisited Optim. Lett. 7 221-229
  • [2] Lalitha CS(1979)Tangent cones, generalized gradients and mathematical programming in Banach spaces Math. Oper. Res. 4 79-97
  • [3] Hirriart-Urruty JB(1979)New concepts in nondifferentiable programming Bull. Soc. Math. France 60 57-85
  • [4] Hirriart-Urruty JB(2017)Necessary and sufficient KKT optimality conditions in non-convex optimization Optim. Lett. 11 41-46
  • [5] Ho Q(2018)Characterization of (weakly/properly/robust) efficient solutions in nonsmooth semi-infinite multiobjective optimization using convexificators Optimization 67 217-235
  • [6] Kabgani A(2017)Optimality conditions in optimization problems with convex feasible set using convexificators Math. Methods Oper. Res. 86 103-121
  • [7] Soleimani-damaneh M(2010)Revisiting Tietze–Nakajima: local and global convexity for maps Can. J. Math. 62 975-993
  • [8] Kabgani A(2010)On representations of the feasible set in convex optimization Optim. Lett. 4 1-5
  • [9] Soleimani-damaneh M(1986)An introduction to the theory of nonsmooth optimization Optimization 17 827-858
  • [10] Zamani M(2006)Optimality conditions for quasiconvex programs SIAM J. Optim. 17 500-510
12