We study the sets of Pareto-optimal and weakly Pareto-optimal solutions to a vector maximization problem defined by a continuous vector-valued quasiconcave criterion functionf and a closed convex set of alternativesS....
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We study the sets of Pareto-optimal and weakly Pareto-optimal solutions to a vector maximization problem defined by a continuous vector-valued quasiconcave criterion functionf and a closed convex set of alternativesS. IfS is compact, it is shown that the set of weakly Pareto-optimal alternatives is connected, but that the set of Pareto-optimal alternatives is not necessarily connected. However, the set of Pareto optima is shown to be connected for some important subclasses of quasiconcave functions. We also provide some reasonable conditions under which the compactness assumption onS may be relaxed and connectedness maintained.
作者：
BENSON, HPAssociate Professor
Department of Management and Administrative Sciences University of Florida Gainesville Florida
In this note, we give sufficient conditions for a domination property to hold for a vector maximization problem with respect to cones. A previously developed result concerning this domination property easily follows f...
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In this note, we give sufficient conditions for a domination property to hold for a vector maximization problem with respect to cones. A previously developed result concerning this domination property easily follows from these conditions. We also show that, if one of these conditions is relaxed, then the domination property may not hold.
作者：
GEARHART, WBAssociate Professor
Division of Mathematics Computer Science and Systems Design University of Texas at San Antonio San Antonio Texas
A general class of scalarization methods for multiple-objective optimization is presented. It is then shown how the optimal solutions characterize the properly efficient points.
A general class of scalarization methods for multiple-objective optimization is presented. It is then shown how the optimal solutions characterize the properly efficient points.
The purpose of the present note is to provide a somewhat more flexible statement of the sufficiency conditions in Section 4 of Ref. 1 and to give explicit statements of the fundamental necessity and sufficiency result...
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The purpose of the present note is to provide a somewhat more flexible statement of the sufficiency conditions in Section 4 of Ref. 1 and to give explicit statements of the fundamental necessity and sufficiency results, which were only implicitly presented there. The additional flexibility is obtained by considering local, rather than global, pseudoconcavity requirements.
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