Existence of Solutions and Algorithms for Bilevel Vector Equilibrium Problems: An Auxiliary Principle Technique

Ouayl Chadli (), Qamrul Hasan Ansari () and Suliman Al-Homidan ()
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Ouayl Chadli: Ibn Zohr University
Qamrul Hasan Ansari: Aligarh Muslim University
Suliman Al-Homidan: King Fahd University of Petroleum and Minerals

Journal of Optimization Theory and Applications, 2017, vol. 172, issue 3, No 2, 726-758

Abstract: Abstract The main goal of this paper is to introduce and study bilevel vector equilibrium problems. We first establish some existence results for solutions of vector equilibrium problems and mixed vector equilibrium problems. We study the existence of solutions of bilevel vector equilibrium problems by considering a vector Thikhonov-type regularization procedure. By using this regularization procedure and existence results for mixed vector equilibrium problems, we establish some existence results for solutions of bilevel vector equilibrium problems. By using the auxiliary principle, we propose an algorithm for finding the approximate solutions of bilevel vector equilibrium problems. The strong convergence of the proposed algorithm is also studied.

Keywords: Bilevel vector equilibrium problems; Mixed vector equilibrium problems; Vector equilibrium problems; Bilevel programs; Auxiliary principle; C-maximal bifunctions; C-monotone bifunctions; C-convex functions; C-upper (lower) semicontinuity; Convergence analysis; 90C30; 90C29; 90C33; 49J40; 47J20 (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10957-017-1062-y

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