Set-Valued Analysis

, Volume 14, Issue 4, pp 413–424 | Cite as

Some Properties of General Minimization Problems with Constraints

  • Vy K. LeEmail author
  • Dumitru Motreanu


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 words

minimization problems constraints Palais–Smale condition 


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Copyright information

© Springer Science+Business Media B.V. 2006

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsUniversity of Missouri-RollaRollaUSA
  2. 2.Département de MathématiquesUniversité de PerpignanPerpignanFrance

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