We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
Multiobjective problems of convex geometry.
- Authors
Kutateladze, S. S.
- 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.
- Subjects
CALCULUS of variations; CONVEX geometry; PARETO optimum; EXTREMAL problems (Mathematics); FILM boiling
- Publication
Siberian Mathematical Journal, 2009, Vol 50, Issue 5, p887
- ISSN
0037-4466
- Publication type
Article
- DOI
10.1007/s11202-009-0099-z