Acta mathematica scientia,Series A ›› 2009, Vol. 29 ›› Issue (3): 800-809.

• Articles • Previous Articles     Next Articles

Henig Proper Efficiency in the ic-Conen-Convexlike Set-valued Optimization Problems

  

  1. (Research Institute of Information and System Computation Science, North National University, Ningxia |Yinchuan 750021);(Department of Mathematics, Luoyang Normal College, Henan Luoyang 471022)
  • Received:2007-01-25 Revised:2008-11-05 Online:2009-06-25 Published:2009-06-25
  • Supported by:

    宁夏高等学校科学研究项目(2007JY008)、河南省教育厅自然科学研究项目(2007110024)和北方民族大学校内科研项目(2007y045)资助

Abstract:

In this paper, the set-valued vector optimization problems with constraint in locally convex spaces is studied. Under the assumption of the
ic-cone-convexlikeness, the optimality conditions for Henig proper efficient solutions are established in terms of scalarization and Lagrange multipliers. After introducing the new concept of Henig proper saddle-point for an appropriate set-valued Lagrange map, we use it to charactertize the Henig proper efficiency. In addition, a scalar Lagrange dual model for set-valued optimization is presented, and the dual theorems are obtained in sense of Henig proper efficiency. All the results   obtained in this paper are proven under the conditions that the constraint cone need not to have a nonempty interior.

Key words: Set-valued map, ic-cone-convexlikeness, Henig proper efficiency, Saddle-point, Duality

CLC Number: 

  • 90C26
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