New closedness results for efficient sets in multiple objective mathematical programming

被引:8
作者
Benson, HP [1 ]
Sun, EJ [1 ]
机构
[1] Univ Florida, Dept Informat & Decis Sci, Gainesville, FL 32611 USA
关键词
D O I
10.1006/jmaa.1999.6541
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
There are various theoretical, algorithmic, and practical reasons for developing necessary and sufficient conditions for the efficient set of a multiple objective mathematical programming problem (P) to be closed. Yet only a small number of results of this type, limited to special cases of Problem (P), have been developed. In this article we present a necessary condition and several sufficient conditions for the closedness of the efficient sets of more general cases of Problem (P) than have heretofore been studied. Our approach relies in part upon generalizing the concepts of quasi-concavity and strict quasi-concavity for real-valued functions to vector-valued functions. Our approach also relies upon some new characterizations of an efficient solution for Problem (P) that we develop in the article. (C) 1999 Academic Press.
引用
收藏
页码:277 / 296
页数:20
相关论文
共 46 条
[1]   FINDING ALL MAXIMAL EFFICIENT FACES IN MULTIOBJECTIVE LINEAR-PROGRAMMING [J].
ARMAND, P .
MATHEMATICAL PROGRAMMING, 1993, 61 (03) :357-375
[2]   DETERMINATION OF THE EFFICIENT SET IN MULTIOBJECTIVE LINEAR-PROGRAMMING [J].
ARMAND, P ;
MALIVERT, C .
JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 1991, 70 (03) :467-489
[3]  
Benayoun J. T. R., 1971, MATH PROGRAM, V1, P366, DOI DOI 10.1007/BF01584098
[4]   OPTIMIZATION OVER THE EFFICIENT SET [J].
BENSON, HP .
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1984, 98 (02) :562-580
[5]  
Benson HP, 1990, J GLOBAL OPTIM, V1, P83, DOI 10.1007/BF00120667
[6]   MINIMIZATION OF A QUASI-CONCAVE FUNCTION OVER AN EFFICIENT SET [J].
BOLINTINEANU, S .
MATHEMATICAL PROGRAMMING, 1993, 61 (01) :89-110
[7]  
Chankong V., 1983, Multiobjective Decision Making: Theory and Methodology
[8]   CONNECTEDNESS IN MULTIPLE LINEAR FRACTIONAL-PROGRAMMING [J].
CHOO, EU ;
ATKINS, DR .
MANAGEMENT SCIENCE, 1983, 29 (02) :250-255
[9]  
Cohon J., 1978, Multiobjective programming and planning
[10]   Connectedness of the efficient set for three-objective quasiconcave maximization problems [J].
Daniilidis, A ;
Hadjisavvas, N ;
Schaible, S .
JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 1997, 93 (03) :517-524