Journal
SET-VALUED ANALYSIS
Volume 12, Issue 1-2, Pages 163-193Publisher
KLUWER ACADEMIC PUBL
DOI: 10.1023/B:SVAN.0000023398.73288.82
Keywords
variational analysis; nonsmooth optimization; generalized differentiation; lower and upper subgradients; infinite-dimensional spaces; necessary optimality conditions; mathematical programs with equilibrium constraints
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The paper concerns first-order necessary optimality conditions for problems of minimizing nonsmooth functions under various constraints in infinite-dimensional spaces. Based on advanced tools of variational analysis and generalized differential calculus, we derive general results of two independent types called lower subdifferential and upper subdifferential optimality conditions. The former ones involve basic/limiting subgradients of cost functions, while the latter conditions are expressed via Frechet/regular upper subgradients in fairly general settings. All the upper subdifferential and major lower subdifferential optimality conditions obtained in the paper are new even in finite dimensions. We give applications of general optimality conditions to mathematical programs with equilibrium constraints deriving new results for this important class of intrinsically nonsmooth optimization problems.
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