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Optimization over and connectedness of the efficient set(s)
Abstract
The first problem considered in this paper, (P), is that of maximizing a continuous function over the set of Pareto-optimal solutions from a multiple objective linear programming (MOLP) problem. By relaxing the domain to the convex one of the MOLP problem, we are able to introduce a supplementary parametric programming problem, which is motivated by the results of Benson. In general, a solution to the supplementary problem provides an upper bound for (P) which is nonincreasing in the parameter. When the objective is convex and the domain is polyhedral, the upper bound yields the exact solution for some finite value of the parameter. In the linearly dependent case, this finite value is easily predetermined. In the second problem considered in this paper we study the connectedness of the sets of efficient alternatives and efficient outcomes to a vector maximization problem defined by a continuous vector-valued function f on a closed convex domain. We consider a variety of generalized cone-concave functions. Numerous results and examples are presented depending upon the specific nature of f and its domain.
Subject Area
Mathematics
Recommended Citation
Fosnaugh, Timothy Alan, "Optimization over and connectedness of the efficient set(s)" (1993). ETD collection for University of Nebraska-Lincoln. AAI9402391.
https://digitalcommons.unl.edu/dissertations/AAI9402391