J Optim Theory Appl https://doi.org/10.1007/s10957-018-1321-6 Optimality Conditions for Vector Equilibrium Problems with Applications 1 2 Alfredo Iusem · Felipe Lara Received: 22 September 2017 / Accepted: 22 May 2018 © Springer Science+Business Media, LLC, part of Springer Nature 2018 Abstract We use asymptotic analysis for studying noncoercive pseudomonotone equilibrium problems and vector equilibrium problems. We introduce suitable notions of asymptotic functions, which provide sufﬁcient conditions for the set of solutions of these problems to be nonempty and compact under quasiconvexity of the objec- tive function. We characterize the efﬁcient and weakly efﬁcient solution set for the nonconvex vector equilibrium problem via scalarization. A sufﬁcient condition for the closedness of the image of a nonempty, closed and convex set via a quasicon- vex vector-valued function is given. Finally, applications to the quadratic fractional programming problem are also presented. Keywords Asymptotic analysis · Generalized convexity · Pseudomonotone operators · Equilibrium problems · Vector optimization Mathematics Subject Classiﬁcation 90C20 · 90C26 · 90C32 1 Introduction Equilibrium problems were introduced in the pioneer work of Ky Fan , and deeply studied along the years (see [2,3] among others). They encompass several problems found in ﬁxed point theory, optimization and nonlinear analysis, e.g., minimization
Journal of Optimization Theory and Applications – Springer Journals
Published: Jun 4, 2018
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