Results 1 to 10 of about 34 (31)
A new kind of inner superefficient points [PDF]
Journal of Inequalities and Applications, 2017 In this paper, some properties of the interior of positive dual cones are discussed. With the help of dilating cones, a new notion of inner superefficient points for a set is introduced.
Yihong Xu, Lei Wang, Chunhui Shao
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Approximate weakly efficient solutions of set-valued vector equilibrium problems [PDF]
Journal of Inequalities and Applications, 2018 In this paper, we introduce a new kind of approximate weakly efficient solutions to the set-valued vector equilibrium problems with constraints in locally convex Hausdorff topological vector spaces; then we discuss a relationship between the weakly ...
Jian Chen, Yihong Xu, Ke Zhang
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Approximate Benson efficient solutions for set-valued equilibrium problems
Journal of Inequalities and Applications, 2020 In locally convex Hausdorff topological vector spaces, the approximate Benson efficient solution is proposed for set-valued equilibrium problems and its relationship to the Benson efficient solution is discussed.
Shasha Hu, Yihong Xu, Zhichao Niu
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ε‐Properly Efficiency of Multiobjective Semidefinite Programming with Set‐Valued Functions
Mathematical Problems in Engineering, Volume 2017, Issue 1, 2017., 2017 In this paper, we study the ε‐properly efficiency of multiobjective semidefinite programming with set‐valued functions. Firstly, we obtain the scalarization theorems under the condition of the generalized cone‐subconvexlikeness. Then, we establish the alternative theorem which contains matrixes and vectors, the ε‐Lagrange multiplier theorems, and the ε‐
Chun Hong Yuan +2 more
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A Characterization of E‐Benson Proper Efficiency via Nonlinear Scalarization in Vector Optimization
Journal of Applied Mathematics, Volume 2014, Issue 1, 2014., 2014 A class of vector optimization problems is considered and a characterization of E‐Benson proper efficiency is obtained by using a nonlinear scalarization function proposed by Göpfert et al. Some examples are given to illustrate the main results.
Ke Quan Zhao +3 more
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Abstract and Applied Analysis, Volume 2013, Issue 1, 2013., 2013 A new notion of the ic‐cone convexlike set‐valued map characterized by the algebraic interior and the vector closure is introduced in real ordered linear spaces. The relationship between the ic‐cone convexlike set‐valued map and the nearly cone subconvexlike set‐valued map is established.
Zhi-Ang Zhou, Graziano Crasta
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Existence Theorems for Vector Equilibrium Problems via Quasi‐Relative Interior
The Scientific World Journal, Volume 2013, Issue 1, 2013., 2013 The aim of this paper is to present new existence theorems for solutions of vector equilibrium problems, by using weak interior type conditions and weak convexity assumptions.
Capătă Adela Elisabeta +3 more
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ϵ‐Henig Saddle Points and Duality of Set‐Valued Optimization Problems in Real Linear Spaces
The Scientific World Journal, Volume 2013, Issue 1, 2013., 2013 We study ϵ‐Henig saddle points and duality of set‐valued optimization problems in the setting of real linear spaces. Firstly, an equivalent characterization of ϵ‐Henig saddle point of the Lagrangian set‐valued map is obtained. Secondly, under the assumption of the generalized cone subconvexlikeness of set‐valued maps, the relationship between the ϵ ...
Zhi-Ang Zhou +2 more
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Strict Efficiency in Vector Optimization with Nearly Convexlike Set‐Valued Maps
Abstract and Applied Analysis, Volume 2013, Issue 1, 2013., 2013 The concept of the well posedness for a special scalar problem is linked with strictly efficient solutions of vector optimization problem involving nearly convexlike set‐valued maps. Two scalarization theorems and two Lagrange multiplier theorems for strict efficiency in vector optimization involving nearly convexlike set‐valued maps are established. A
Xiaohong Hu +3 more
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Journal of Applied Mathematics, Volume 2012, Issue 1, 2012., 2012 We first introduce a new notion of the partial and generalized cone subconvexlike set‐valued map and give an equivalent characterization of the partial and generalized cone subconvexlike set‐valued map in linear spaces. Secondly, a generalized alternative theorem of the partial and generalized cone subconvexlike set‐valued map was presented.
Zhi-Ang Zhou +2 more
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