Continuity and closedness of constraint and solution set mappings in unified parametric semi-infinite vector optimization

In general Banach spaces, we consider a vector optimization problem (SVOP) in which the objective is a set-valued mapping whose graph is the union of finitely many polyhedra or the union of finitely many generalized polyhedra. Dropping the compactness assumption, we establish some results on structure of the weak Pareto solution set, Pareto solution set, weak Pareto optimal value set, and Pareto optimal value set of (SVOP) and on connectedness of Pareto solution set and Pareto optimal value set of (SVOP). In particular, we improved and generalize, Arrow, Barankin, and Blackwell’s classical results in Euclidean spaces and Zheng and Yang’s results in general Banach spaces.

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Connectedness of the efficient solution set of a convex vector optimization in normed spaces

Nonlinear Analysis ◽

10.1016/0362-546x(94)90095-7 ◽

1994 ◽

Vol 23 (9) ◽

pp. 1105-1114 ◽

Cited By ~ 11

Author(s):

Gong Xunhua

Keyword(s):

Vector Optimization ◽

Efficient Solution ◽

Solution Set ◽

Normed Spaces ◽

Convex Vector Optimization ◽

Efficient Solution Set

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Characterizing Nonemptiness and Compactness of the Solution Set of a Convex Vector Optimization Problem with Cone Constraints and Applications

Journal of Optimization Theory and Applications ◽

10.1007/s10957-004-5155-z ◽

2004 ◽

Vol 123 (2) ◽

pp. 391-407 ◽

Cited By ~ 11

Author(s):

X. X. Huang ◽

X. Q. Yang ◽

K. L. Teo

Keyword(s):

Vector Optimization ◽

Optimization Problem ◽

Vector Optimization Problem ◽

Solution Set ◽

Cone Constraints ◽

Convex Vector Optimization

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Continuity of the solution set mappings to a parametric set optimization problem

Optimization Letters ◽

10.1007/s11590-014-0738-6 ◽

2014 ◽

Vol 8 (8) ◽

pp. 2315-2327 ◽

Cited By ~ 16

Author(s):

Y. D. Xu ◽

S. J. Li

Keyword(s):

Optimization Problem ◽

Solution Set ◽

Set Optimization ◽

Set Optimization Problem ◽

Set Mappings

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Coderivatives and Aubin property of efficient point and efficient solution set-valued maps in parametric vector optimization

Journal of Inequalities and Applications ◽

10.1186/s13660-020-02499-2 ◽

2020 ◽

Vol 2020 (1) ◽

Author(s):

Xiaowei Xue

Keyword(s):

Explicit Expression ◽

Vector Optimization ◽

Efficient Solution ◽

Vector Optimization Problem ◽

Solution Set ◽

Efficient Point ◽

Aubin Property ◽

Parametric Vector Optimization ◽

Whole Space ◽

Efficient Solution Set

Abstract The aim of this paper is computing the coderivatives of efficient point and efficient solution set-valued maps in a parametric vector optimization problem. By using a method different from the existing literature we establish an upper estimate and explicit expression for the coderivatives of an efficient point set-valued map where the independent variable can take values in the whole space. As an application, we give some characterizations on the Aubin property of an efficient point map and an explicit expression of the coderivative for an efficient solution map. We provide several examples illustrating the main results.

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