New Scalarizing Approach to the Stability Analysis in Parametric Generalized Ky Fan Inequality Problems

Pham Huu Sach () and Le Anh Tuan ()
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Pham Huu Sach: Hanoi Institute of Mathematics
Le Anh Tuan: Nong Lam University

Journal of Optimization Theory and Applications, 2013, vol. 157, issue 2, No 3, 347-364

Abstract: Abstract This paper gives sufficient conditions for the upper and lower semicontinuities of the solution mapping of a parametric mixed generalized Ky Fan inequality problem. We use a new scalarizing approach quite different from traditional linear scalarization approaches which, in the framework of the stability analysis of solution mappings of equilibrium problems, were useful only for weak vector equilibrium problems and only under some convexity and strict monotonicity assumptions. The main tools of our approach are provided by two generalized versions of the nonlinear scalarization function of Gerstewitz. Our stability results are new and are obtained by a unified technique. An example is given to show that our results can be applied, while some corresponding earlier results cannot.

Keywords: Nonlinear scalarization function; Ky Fan inequality problem; Set-valued map; Semicontinuity; Strict monotonicity (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s10957-012-0105-7

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