Acta mathematica scientia,Series B ›› 2010, Vol. 30 ›› Issue (4): 1154-1166.doi: 10.1016/S0252-9602(10)60113-0

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SEPARABLE CONDITIONS AND SCALARIZATION OF BENSON PROPER EFFICIENCY

 QIU Jing-Hui, HAO Yuan, WANG Cui   

  1. Department of Mathematics, Suzhou University, Suzhou 215006, China
  • Received:2007-09-07 Revised:2008-08-11 Online:2010-07-20 Published:2010-07-20
  • Supported by:

    Supported by the National Natural Science Foundation of China (10571035, 10871141)

Abstract:

Under the assumption that the ordering cone has a nonempty interior and is separable (or the feasible set has a
nonempty interior and is separable), we give scalarization theorems on Benson proper efficiency. Applying the results to vector optimization problems with nearly cone-subconvexlike set-valued maps, we obtain scalarization theorems and Lagrange multiplier theorems for Benson proper efficient solutions.

Key words: Locally convex space, nearly cone-subconvexlike set-valued map, Benson proper efficiency, scalarization

CLC Number: 

  • 90C29
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