期刊
SIAM JOURNAL ON OPTIMIZATION
卷 21, 期 2, 页码 597-614出版社
SIAM PUBLICATIONS
DOI: 10.1137/090747117
关键词
constrained optimization; composite optimization; Mangasarian-Fromovitz constraint qualification; active set; identification
资金
- National Science Foundation [DMS-0806057, CCF-0430504, DMS-0914524]
Identification of active constraints in constrained optimization is of interest from both practical and theoretical viewpoints, as it holds the promise of reducing an inequality-constrained problem to an equality-constrained problem, in a neighborhood of a solution. We study this issue in the more general setting of composite nonsmooth minimization, in which the objective is a composition of a smooth vector function c with a lower semicontinuous function h, typically nonsmooth but structured. In this setting, the graph of the generalized gradient. h can often be decomposed into a (nondisjoint) union of simpler subsets. Identification amounts to deciding which subsets of the graph are active in the criticality conditions at a given solution. We give conditions under which any convergent sequence of approximate critical points finitely identifies the activity. Prominent among these properties is a condition akin to the Mangasarian-Fromovitz constraint qualification, which ensures boundedness of the set of multiplier vectors that satisfy the optimality conditions at the solution.
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