Journal
SIAM JOURNAL ON OPTIMIZATION
Volume 24, Issue 3, Pages 1344-1381Publisher
SIAM PUBLICATIONS
DOI: 10.1137/130906878
Keywords
variational analysis and optimization; first-order and second-order generalized differentiation; Lipschitzian and Holderian stability; nonlinear programming; second-order growth and constraint qualifications; polyhedric constraints; optimal control; semilinear elliptic PDEs
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Funding
- National Science Foundation [DMS-1007132]
- Australian Research Council [DP-12092508]
- Portuguese Foundation of Science and Technologies [MAT/11109]
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [1007132] Funding Source: National Science Foundation
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The paper concerns a systematic study of full stability in general optimization models including its conventional Lipschitzian version as well as the new Holderian one. We derive various characterizations of both Lipschitzian and Holderian full stability in nonsmooth optimization, which are new in finite-dimensional and infinite-dimensional frameworks. The characterizations obtained are given in terms of second-order growth conditions and also via second-order generalized differential constructions of variational analysis. We develop effective applications of our general characterizations of full stability to conventional models of nonlinear programming, to optimization problems with polyhedric constraints in infinite dimensions, and to optimal control problems governed by semilinear elliptic PDEs.
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