Dido's Problem and Pareto Optimality

S. S. Kutateladze (sskutmath.nsc.ru)

Abstract: Under study is the new class of geometrical extremal problems in which it is required to achieve the best result in the presence of conflicting goals; e.g., given the surface area of a convex body~$\mathfrak x$, we try to maximize the volume of~$\mathfrak x$ and minimize the width of~$\mathfrak x$ simultaneously. These problems are addressed along the lines of multiple criteria decision making. We describe the Pareto-optimal solutions of isoperimetric-type vector optimization problems on using the techniques of the space of convex sets, linear majorization, and mixed volumes.

Keywords: isoperimetric problem, vector optimization, Pareto optimum,

Category 1: Other Topics (Multi-Criteria Optimization )

Category 2: Convex and Nonsmooth Optimization (Convex Optimization )

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Entry Submitted: 03/05/2009
Entry Accepted: 03/06/2009
Entry Last Modified: 03/06/2009

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