Taiwanese Journal of Mathematics
- Taiwanese J. Math.
- Volume 16, Number 4 (2012), 1453-1473.
OPTIMALITY CONDITIONS FOR EFFICIENT SOLUTION TO THE VECTOR EQUILIBRIUM PROBLEMS WITH CONSTRAINTS
In this paper, by using the generalization of Ljusternik theorem, the open mapping theorem of convex process, and the convex sets separation theorem, we give the necessary conditions for the efficient solution to the constrained vector equilibrium problems without requiring that the ordering cone in the objective space has a nonempty interior and without requiring that the the convexity conditions. By the assumption of the convexity, we give the sufficient conditions for the efficient solution. As applications, we give the necessary conditions and the sufficient conditions for efficient solution to the constrained vector variational inequalities and constrained vector optimization problems.
Taiwanese J. Math., Volume 16, Number 4 (2012), 1453-1473.
First available in Project Euclid: 18 July 2017
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Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 49J52: Nonsmooth analysis [See also 46G05, 58C50, 90C56] 49J50: Fréchet and Gateaux differentiability [See also 46G05, 58C20] 90C29: Multi-objective and goal programming 90C46: Optimality conditions, duality [See also 49N15]
Gong, Xun-Hua. OPTIMALITY CONDITIONS FOR EFFICIENT SOLUTION TO THE VECTOR EQUILIBRIUM PROBLEMS WITH CONSTRAINTS. Taiwanese J. Math. 16 (2012), no. 4, 1453--1473. doi:10.11650/twjm/1500406743. https://projecteuclid.org/euclid.twjm/1500406743