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Warianty tytułu
Języki publikacji
Abstrakty
We consider a semi-infinite optimization problem in Banach spaces, where both the objective functional and the constraint operator are compositions of convex nonsmooth mappings and differentiable mappings. We derive necessary optimality conditions for these problems. Finally, we apply these results to non-convex stochastic optimization problems with stochastic dominance constraints, generalizing earlier results.
Czasopismo
Rocznik
Tom
Strony
633--646
Opis fizyczny
Bibliogr. 16 poz.
Twórcy
autor
autor
- Stevens Institute of Technology, Department of Mathematical Sciences, Hoboken, NJ, USA, darinka.dentcheva@stevens.edu
Bibliografia
- BILLINGSLEY, P. (1995) Probability and Measure. John Wiley & Sons, New York.
- BONNANS, J.F. and COMINETTI, R. (1996) Perturbed optimization in Banach spaces. III. Semi-infinite optimization. SIAM J. Control Optim. 34, 1555-1567.
- BONNANS, J.F. and SHAPIRO, A. (2000) Perturbation Analysis of Optimization Problems. Springer-Verlag, New York.
- CASTAING, C. and VALADIER, M. (1977) Convex Analysis and Measurable Multifunctions. Springer-Verlag, Berlin.
- CANOVAS, M.J., DONTCHEV, A.L., LOPEZ, M.A. and PARRA, J. (2005) Metric regularity of semi-infinite constraint systems. Mathematical Programming 104, 329-346.
- DENTCHEVA, D. and RUSZCZYŃSKI, A. (2003) Optimization with stochastic dominance constraints. SIAM Journal on Optimization 14, 548-566.
- DENTCHEVA, D. and RUSZCZYŃSKI, A. (2004) Optimality and duality theory for stochastic optimization problems with nonlinear dominance constraints. Mathematical Programming 99, 329-350.
- GOBERNA, M.A. and LOPEZ, M.A. (1998) Linear Semi-Infinite Optimization. Wiley, Chichester.
- KLATTE, D. and HENRION, R. (1998) Regularity and stability in nonlinear semi-infinite optimization. Nonconvex Optimization and Applications 25, 69-102.
- LEVIN, V.L. (1985) Convex Analysis in Spaces of Measurable Functions and its Applications in Economics. Nauka, Moscow, (in Russian).
- MORDUKHOVICH, B. (2006) Variational Analysis and Generalized Differentiation. Springer-Verlag, Berlin.
- PENOT, J.P. (1994) Optimality conditions in mathematical programming and composite optimization. Mathematical Programming 67, 225-246.
- ROBINSON, S.M. (1976) Stability theory for systems of inequalities. II: Differentiable nonlinear systems. SIAM J. Numer. Anal. 13, 497-513.
- ROCKAFELLAR, R.T. and WETS, R.J.-B. (1998) Variational Analysis. Springer-Verlag, Berlin.
- STUDNIARSKI, M. and JEYAKUMAR, V. (1995) A generalized mean-value theorem and optimality conditions in composite nonsmooth minimization. Nonlinear Analysis 24, 883-894.
- YANG, X.Q. (1998) Second-order global optimality conditions for convex composite optimization. Mathematical Programming 81, 327-347.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BAT5-0017-0059