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Applied Mathematics and Optimization

, Volume 20, Issue 1, pp 71–80 | Cite as

Second-order optimality conditions for the extremal problem under inclusion constraints

  • Pham Huy Dien
  • Pham Huu Sach
Article

Abstract

In this paper we establish second-order necessary and sufficient conditions for the problem of minimizing a functionf on the solution set of an inclusion 0∈F(x) wheref and the support function of set-valued mapF areC1,1-functions, i.e., functions whose gradient mapping is locally Lipschitz. Our results generalize those obtained by Hiriart-Urruty and others.

Keywords

Optimality Condition System Theory Mathematical Method Extremal Problem Support Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag New York Inc 1989

Authors and Affiliations

  • Pham Huy Dien
    • 1
  • Pham Huu Sach
    • 1
  1. 1.Institute of MathematicsHanoiVietnam

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