Generic minimizing behavior in semi-algebraic optimization

Autor:	Drusvyatskiy, D., Ioffe, A. D., Lewis, A. S.
Rok vydání:	2015
Předmět:	Mathematics - Optimization and Control 49K40 90C31 14P10 32B20
Druh dokumentu:	Working Paper
Popis:	We present a theorem of Sard type for semi-algebraic set-valued mappings whose graphs have dimension no larger than that of their range space: the inverse of such a mapping admits a single-valued analytic localization around any pair in the graph, for a generic value parameter. This simple result yields a transparent and unified treatment of generic properties of semi-algebraic optimization problems: "typical" semi-algebraic problems have finitely many critical points, around each of which they admit a unique "active manifold" (analogue of an active set in nonlinear optimization); moreover, such critical points satisfy strict complementarity and second-order sufficient conditions for optimality are indeed necessary. Comment: 25 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1504.07694 Zobrazit plný text záznamu View this record from Arxiv