Some Properties of General Minimization Problems with Constraints
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The paper studies the existence of solutions and necessary conditions of optimality for a general minimization problem with constraints. Although we focus mainly on the case where the cost functional is locally Lipschitz, a general Palais–Smale condition is proposed and some of its properties are studied. Applications to an optimal control problem and a Lagrange multiplier rule are also given.
Key wordsminimization problems constraints Palais–Smale condition
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- 3.Aizicovici, S., Motreanu, D., Pavel, N.H.: Fully nonlinear programming problems with closed range operators. Lecture Notes in Pure and Appl. Math. 225, Dekker, New York (2002)Google Scholar
- 6.Brézis, H.: Analyse Fonctionnelle. Théorie et Applications. Masson, Paris (1983)Google Scholar
- 14.Le, V.K., Motreanu, D.: On a general minimization problem with constraints. Proc. Conference on Differential and Difference Equations and Applications, Melbourne FL, 07/2005 (submitted)Google Scholar
- 15.Li, S.J.: An existence theorem on multiple critical points and its application in nonlinear P. D. E. Acta Math. Sci. 4 (1984)Google Scholar
- 19.Mordukhovich, B.S.: Variational Analysis and Generalized Differentiation, Vol I, II. Springer, Berlin Heidelberg New York (2006)Google Scholar
- 22.Willem, M.: An introduction to critical point theory, Lecture notes, SMR 281/5211, I. C. T. P., Trieste (1988)Google Scholar