Second-Order Optimality Conditions for Mathematical Programs with Equilibrium Constraints

Second-Order Optimality Conditions for Mathematical Programs with Equilibrium Constraints. Guo, L., Lin, G., & Ye, J. J. Journal of Optimization Theory and Applications, 158(1):33–64, July, 2013. 58 citations (Semantic Scholar/DOI) [2022-11-30]

Paper doi abstract bibtex

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.

@article{guo_second-order_2013,
	title = {Second-{Order} {Optimality} {Conditions} for {Mathematical} {Programs} with {Equilibrium} {Constraints}},
	volume = {158},
	issn = {0022-3239, 1573-2878},
	url = {http://link.springer.com/10.1007/s10957-012-0228-x},
	doi = {10.1007/s10957-012-0228-x},
	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.},
	language = {en},
	number = {1},
	urldate = {2022-11-29},
	journal = {Journal of Optimization Theory and Applications},
	author = {Guo, Lei and Lin, Gui-Hua and Ye, Jane J.},
	month = jul,
	year = {2013},
	note = {58 citations (Semantic Scholar/DOI) [2022-11-30]},
	keywords = {/unread},
	pages = {33--64},
}

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