Hsia, W. S.; Lee, T. Y. Proper D-solutions of multiobjective programming problems with set functions. (English) Zbl 0595.90084 J. Optimization Theory Appl. 53, 247-258 (1987). A special class of solutions for multiobjective programming problems with set functions is considered. A subset of nondominated solutions, called proper D-solution set, with respect to a given domination structure is characterized under two situations, with and without inequality constraints. Cited in 18 Documents MSC: 90C31 Sensitivity, stability, parametric optimization Keywords:nondominated solutions; proper D-solution set PDF BibTeX XML Cite \textit{W. S. Hsia} and \textit{T. Y. Lee}, J. Optim. Theory Appl. 53, 247--258 (1987; Zbl 0595.90084) Full Text: DOI References: [1] Morris, R. J. T.,Optimal Constrained Selection of Measurable Subset, Journal of Mathematical Analysis and Applications, Vol. 70, pp. 546-562, 1979. · Zbl 0417.49032 [2] Lai, H. L., andYang, S. S.,Saddle Point and Duality in the Optimization Theory of Convex Set Functions, Journal of the Australian Mathematical Society, Series B, Vol. 24, pp. 130-137, 1982. · Zbl 0502.49006 [3] Chou, J. H., Hsia, W. S., andLee, T. Y.,Second-Order Optimality Conditions for Mathematical Programming with Set Functions, Journal of the Australian Mathematical Society, Series B, Vol. 26, pp. 284-292, 1985. · Zbl 0571.90099 [4] Chou, J. H., Hsia, W. S., andLee, T. Y.,On Multiple Objective Programming Problems with Set Functions, Journal of Mathematical Analysis and Applications, Vol. 15, pp. 383-394, 1985. · Zbl 0564.90069 [5] Yu, P. L.,Cone Convexity, Cone Extreme Points, and Nondominated Solutions in Decision Problems with Multiobjectives, Journal of Optimization Theory and Applications, Vol. 14, pp. 319-377, 1974. · Zbl 0268.90057 [6] Tanino, T., andSawaragi, Y.,Duality Theory in Multiobjective Programming, Journal of Optimization Theory and Applications, Vol. 27, pp. 509-529, 1979. · Zbl 0378.90100 [7] Geoffrion, A. M.,Proper Efficiency and Theory of Vector Maximization, Journal of Mathematical Analysis and Applications, Vol. 22, pp. 618-630, 1968. · Zbl 0181.22806 [8] Chou, J. H., Hsia, W. S., andLee, T. Y.,Epigraphs of Convex Set Functions, Journal of Mathematical Analysis and Applications (to appear). · Zbl 0599.49014 [9] Bourbaki, N.,General Topology, Part 1, Addison-Wesley, Reading, Massachusetts, 1966. · Zbl 0145.19302 [10] Rudin, W.,Functional Analysis, McGraw-Hill, New York, New York, 1973. · Zbl 0253.46001 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.