ON THE GENERALIZED FRITZ JOHN OPTIMALITY CONDITIONS OF VECTOR OPTIMIZATION WITH SET-VALUED MAPS UNDER BENSON PROPER EFFICIENCY

Applied Mathematics and Mechanics (English Edition) ›› 2002, Vol. 23 ›› Issue (12): 1444-1451.

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ON THE GENERALIZED FRITZ JOHN OPTIMALITY CONDITIONS OF VECTOR OPTIMIZATION WITH SET-VALUED MAPS UNDER BENSON PROPER EFFICIENCY

SHENG Bao-huai^1,2, LIU San-yang¹

1. Department of Applied Mathematics, Xidian University, Xi’an 710071, P. R. China;
2. Institute of Mathematics, Ningbo University, Ningbo, Zhejiang 315211, P. R. China

Received:2000-03-29 Revised:2005-05-14 Online:2002-12-18 Published:2002-12-18
Supported by:
the National Natural Science Foundation of China(69972036);the Doctor Foundation of Ningbo City

Abstract

Abstract: A kind of tangent derivative and the concepts of strong and weak * pseudoconvexity for a set-valued map are introduced.By the standard separation theorems of the convex sets and cones the optimality Fritz John condition of set-valued optimization under Benson proper efficiency is established,its sufficience is discussed. The form of the optimality conditions obtained here completely tally with the classical results when the set-valued map is specialized to be a single-valued map.

Key words: Contingent tangent cone, set-valued map, Benson proper efficiency, Fritz John condition

2010 MSC Number:

O211.6

SHENG Bao-huai;LIU San-yang. ON THE GENERALIZED FRITZ JOHN OPTIMALITY CONDITIONS OF VECTOR OPTIMIZATION WITH SET-VALUED MAPS UNDER BENSON PROPER EFFICIENCY. Applied Mathematics and Mechanics (English Edition), 2002, 23(12): 1444-1451.

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ON THE GENERALIZED FRITZ JOHN OPTIMALITY CONDITIONS OF VECTOR OPTIMIZATION WITH SET-VALUED MAPS UNDER BENSON PROPER EFFICIENCY

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