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

作者：Pham Huu Sach^*; Le Anh Tuan

来源：Journal of Optimization Theory and Applications, 2013, 157(2): 347-364.

DOI：10.1007/s10957-012-0105-7

• Nonlinear scalarization function
• Ky Fan inequality problem
• Set-valued map
• Semicontinuity
• Strict monotonicity

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.

• 出版日期2013-5