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Second-Order Optimality Conditions for Mathematical Programs with Equilibrium Constraints |
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| Authors: | Lei Guo Gui-Hua Lin Jane J. Ye |
| Affiliation: | 1. School of Mathematical Sciences, Dalian University of Technology, Dalian, 116024, China 2. School of Management, Shanghai University, Shanghai, 200444, China 3. Department of Mathematics and Statistics, University of Victoria, Victoria, BC, V8W 3P4, Canada |
| Abstract: | We study second-order optimality conditions for mathematical programs with equilibrium constraints (MPEC). Firstly, we improve some second-order optimality conditions for standard nonlinear programming problems using some newly discovered constraint qualifications in the literature, and apply them to MPEC. Then, we introduce some MPEC variants of these new constraint qualifications, which are all weaker than the MPEC linear independence constraint qualification, and derive several second-order optimality conditions for MPEC under the new MPEC constraint qualifications. Finally, we discuss the isolatedness of local minimizers for MPEC under very weak conditions. |
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