OPTIMALITY CONDITIONS FOR DIRECTIONALLY DIFFERENTIABLE MULTIOBJECTIVE PROGRAMMING-PROBLEMS

被引：19

作者：

ISHIZUKA, Y

机构：

[1] Department of Mechanical Engineering, Faculty of Science and Technology, Sophia University, Tokyo

来源：

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS | 1992年 / 72卷 / 01期

关键词：

MULTIOBJECTIVE PROGRAMMING; DIRECTIONAL DERIVATIVES; PROPER EFFICIENCY; OPTIMALITY CONDITIONS;

D O I：

10.1007/BF00939951

中图分类号：

C93 [管理学]; O22 [运筹学];

学科分类号：

070105 ; 12 ; 1201 ; 1202 ; 120202 ;

摘要：

This paper is concerned with the optimality for multi-objective programming problems with nonsmooth and nonconvex (but directionally differentiable) objective and constraint functions. The main results are Kuhn-Tucker type necessary conditions for properly efficient solutions and weakly efficient solutions. Our proper efficiency is a natural extension of the Kuhn-Tucker one to the nonsmooth case. Some sufficient conditions for an efficient solution to be proper are also given. As an application, we derive optimality conditions for multi-objective programming problems including extremal-value functions.

引用

页码：91 / 111

页数：21

共 18 条

[1]

Clarke F.H., 1983, OPTIMIZATION NONSMOO

[2]

Demyanov VF, 1980, SOV MATH DOKL, V21, P14

[3]

Fiacco A.V., 1983, MATH PROGRAMMING DAT, V2, P65

[4] CHARACTERIZATION THEOREMS FOR CONSTRAINED APPROXIMATION PROBLEMS VIA OPTIMIZATION THEORY [J].

GEHNER, KR .

JOURNAL OF APPROXIMATION THEORY, 1975, 14 (01) :51-76

[5] PROPER EFFICIENCY AND THEORY OF VECTOR MAXIMIZATION [J].

GEOFFRION, AM .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1968, 22 (03) :618-+

[6] FARKAS THEOREM OF NONCONVEX TYPE AND ITS APPLICATION TO A MIN-MAX PROBLEM [J].

ISHIZUKA, Y .

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 1988, 57 (02) :341-354

[7] NECESSARY AND SUFFICIENT CONDITIONS FOR THE EFFICIENT SOLUTIONS OF NONDIFFERENTIABLE MULTIOBJECTIVE PROBLEMS [J].

ISHIZUKA, Y ;

SHIMIZU, K .

IEEE TRANSACTIONS ON SYSTEMS MAN AND CYBERNETICS, 1984, 14 (04) :625-629

[8] OPTIMALITY CONDITIONS FOR QUASI-DIFFERENTIABLE PROGRAMS WITH APPLICATION TO 2-LEVEL OPTIMIZATION [J].

ISHIZUKA, Y .

SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 1988, 26 (06) :1388-1398

[9] NECESSARY CONDITIONS FOR OPTIMALITY OF NONDIFFERENTIABLE CONVEX MULTIOBJECTIVE PROGRAMMING [J].

KANNIAPPAN, P .

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 1983, 40 (02) :167-174

[10]

Kuhn H.W., 1951, P 2 BERK S MATH STAT, P481

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