Acta mathematica scientia,Series A ›› 2015, Vol. 35 ›› Issue (5): 927-935.

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A New Notion of Generalized Subgradients and Its Properties

Huang Zhenggang   

  1. College of Mathematics and Statistics, Chongqing University of Technology, Chongqing 400054
  • Received:2014-04-20 Revised:2015-03-04 Online:2015-10-25 Published:2015-10-25

Abstract:

This paper proposes a new notion of generalized subgradients and discusses some properties of it in terms of Tangent cone. Using some of those properties, necessary and sufficient optimality conditions for a nonconvex and nondifferentiable scalar optimization problem with inequalities constraints and an arbitrary set constraint are derived, also a necessary condition for a nonconvex and nondifferentiable unconstrained scalar optimization problem is derived.

Key words: k-Lower(upper)subgradient, Tangent cone, Strict local minimizer of order k, Local minimizer, Optimality conditions

CLC Number: 

  • O224
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