Optimality Conditions for Vector Equilibrium Problems with Applications

Alfredo Iusem () and Felipe Lara ()
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Alfredo Iusem: Instituto Nacional de Matemática Pura e Aplicada (IMPA)
Felipe Lara: Universidad de Tarapacá

Journal of Optimization Theory and Applications, 2019, vol. 180, issue 1, No 11, 187-206

Abstract: 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 objective 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 quasiconvex 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; 90C20; 90C26; 90C32 (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (11)

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DOI: 10.1007/s10957-018-1321-6

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