Differential stability properties in convex scalar and vector optimization

被引：0
作者：
D. T. V. An
C. Gutiérrez
机构：
[1] Vietnam Academy of Science and Technology,Institute of Mathematics
[2] Thai Nguyen University of Sciences,Department of Mathematics and Informatics
[3] University of Valladolid,IMUVA (Mathematics Research Institute of the University of Valladolid)
[4] Edificio LUCIA,undefined
来源：
Set-Valued and Variational Analysis | 2021年 / 29卷
关键词：
Differential stability; -subdifferential; Parametric convex programming; Limiting calculus rule; Optimal value function; Approximate solution; Vector optimization; Infimal set; Cone proper set; Weak minimal solution; 49J53; 90C31; 90C25; 90C29;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
This paper focuses on formulas for the ε-subdifferential of the optimal value function of scalar and vector convex optimization problems. These formulas can be applied when the set of solutions of the problem is empty. In the scalar case, both unconstrained problems and problems with an inclusion constraint are considered. For the last ones, limiting results are derived, in such a way that no qualification conditions are required. The main mathematical tool is a limiting calculus rule for the ε-subdifferential of the sum of convex and lower semicontinuous functions defined on a (non necessarily reflexive) Banach space. In the vector case, unconstrained problems are studied and exact formulas are derived by linear scalarizations. These results are based on a concept of infimal set, the notion of cone proper set and an ε-subdifferential for convex vector functions due to Taa.
引用
收藏
页码：893 / 914
页数：21
相关论文
共 54 条
  • [1] An DTV(2020)Differential stability of convex optimization problems under weaker conditions Optimization 69 385-399
  • [2] Köbis MA(2016)Further results on differential stability of convex optimization problems J. Optim. Theory Appl. 170 28-42
  • [3] Tuyen NV(2019)Differential stability of convex optimization problems with possibly empty solution sets J. Optim. Theory Appl. 181 126-143
  • [4] An DTV(2015)Differential stability of convex optimization problems under inclusion constraints Appl. Anal. 94 108-128
  • [5] Yao J-C(1978)Infima of sets in the plane and applications to vectorial optimization Rev. Roumaine Math. Pures Appl. 23 343-360
  • [6] An DTV(2021)Decomposition algorithms for some deterministic and two-stage stochastic single-leader multi-follower games Comput. Optim. Appl. 78 675-704
  • [7] Yao J-C(1965)On the subdifferentiability of convex functions Proc. Amer. Math. Soc. 16 605-611
  • [8] An DTV(1978)Existence theorems for Pareto optimization; multivalued and Banach space valued functionals Trans. Amer. Math. Soc. 244 37-65
  • [9] Yen ND(2019)Optimality conditions for weak solutions of vector optimization problems through quasi interiors and improvement sets J. Nonlinear Convex Anal. 20 2507-2523
  • [10] Bacopoulos A(2017)Sequential ε-subdifferential calculus for scalar and vector mappings Set-Valued Var. Anal. 25 383-403
123456