Oil minmax programming problems containing n-set functions

In this paper, we prove that some sufficient optimality conditions and several duality results of Zalmai [24] are true under more general assumptions than convexity. Here, the generalized convexity is defined by use of sublinear functionals which satisfy certain convexity-type conditions.

[1]  Jean-Philippe Vial,et al.  Strong and Weak Convexity of Sets and Functions , 1983, Math. Oper. Res..

[2]  H. W. Corley,et al.  A Partitioning Problem with Applications in Regional Design , 1972, Oper. Res..

[3]  Wei-Shen Hsia,et al.  On multiple objective programming problems with set functions , 1985 .

[4]  Wei-Shen Hsia,et al.  ProperD-solutions of multiobjective programming problems with set functions , 1987 .

[5]  H. W. Corley,et al.  Duality Relationships for a Partitioning Problem , 1972 .

[6]  Jean Michel,et al.  Quelques resultats sur l'identification de domaines , 1973 .

[7]  G. J. Zalmai A transposition theorem with applications to constrained optimal control problems , 1989 .

[8]  Robert J. T. Morris,et al.  Optimal constrained selection of a measurable subset , 1979 .

[9]  H. Lai,et al.  Duality in mathematical programming of set functions: On Fenchel duality theorem , 1983 .

[10]  E. S. Pearson,et al.  On the Problem of the Most Efficient Tests of Statistical Hypotheses , 1933 .

[11]  D. Begis,et al.  Application de la méthode des éléments finis à l'approximation d'un problème de domaine optimal. Méthodes de résolution des problèmes approchés , 1975 .

[12]  G. J. Zaimai Optimality conditions and duality for constrained measurable subset selection problems with minmax objective functions , 1989 .

[13]  Kensuke Tanaka,et al.  The Multiobjective Optimization Problem of Set Function , 1984 .

[14]  Tan-Yu Lee,et al.  Epigraphs of convex set functions , 1986 .

[15]  Second order optimality conditions for mathematical prograramming with set functions , 1985, The Journal of the Australian Mathematical Society. Series B. Applied Mathematics.

[16]  H. Lai,et al.  Saddle point and duality in the optimization theory of convex set functions , 1982, The Journal of the Australian Mathematical Society. Series B. Applied Mathematics.

[17]  M. A. Hanson,et al.  Further Generalizations of Convexity in Mathematical Programming , 1982 .

[18]  P. K. C. Wang On a class of optimization problems involving domain variations , 1977 .

[19]  H. W. Corley,et al.  Optimization Theory for n-Set Functions , 1987 .

[20]  Robert V. Hogg,et al.  Introduction to Mathematical Statistics. , 1966 .

[21]  B. Mond Generalized convexity in mathematical programming , 1983, Bulletin of the Australian Mathematical Society.

[22]  G. Dantzig,et al.  On the Fundamental Lemma of Neyman and Pearson , 1951 .