Some Properties of General Minimization Problems with Constraints

被引：0

作者：

Vy K. Le

Dumitru Motreanu

机构：

[1] University of Missouri-Rolla,Department of Mathematics and Statistics

[2] Université de Perpignan,Département de Mathématiques

来源：

Set-Valued Analysis | 2006年 / 14卷

关键词：

minimization problems; constraints; Palais–Smale condition;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

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.

引用

页码：413 / 424

页数：11

共 20 条

[1] Aizicovici S.(1999)Nonlinear programming problems associated with closed range operators Appl. Math. Optim. 40 211-228
[2] Motreanu D.(2004)Nonlinear mathematical programming and optimal control Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal. 11 503-524
[3] Pavel N.H.(1990)A note on Palais–Smale condition and coercivity Differential Integral Equations 3 799-800
[4] Aizicovici S.(1981)Variational methods for nondifferentiable functionals and their applications to partial differential equations J. Math. Anal. Appl. 80 102-129
[5] Motreanu D.(1991)The Palais–Smale condition versus coercivity Nonlinear Anal. 16 371-381
[6] Pavel N.H.(1979)Nonconvex minimization problems Bull. Amer. Math. Soc. (N.S.) 1 443-474
[7] Čaklović L.(1993)A note on Palais–Smale condition in the sense of Szulkin Differential Integral Equations 6 1041-1043
[8] Li S.J.(2000)A weak nonsmooth Palais–Smale condition and coercivity Rend. Circ. Mat. Palermo 49 521-526
[9] Willem M.(2002)Relation between the Palais–Smale condition and coerciveness for multivalued mappings Stud. Univ. Babeş-Bolyai Math. 47 67-72
[10] Chang K.C.(2000)Coerciveness property for a class of non-smooth functionals Z. Anal. Anwendungen 19 1087-1093

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