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


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.


Optimality Condition System Theory Mathematical Method Extremal Problem Support Function 
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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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