Journal
JOURNAL OF GLOBAL OPTIMIZATION
Volume 60, Issue 4, Pages 713-736Publisher
SPRINGER
DOI: 10.1007/s10898-013-0136-0
Keywords
Vector optimization; Multiple objective optimization; Convex programming; Duality; Algorithms; Outer approximation
Funding
- NSF [DMS-1007938]
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [1007938] Funding Source: National Science Foundation
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Two approximation algorithms for solving convex vector optimization problems (CVOPs) are provided. Both algorithms solve the CVOP and its geometric dual problem simultaneously. The first algorithm is an extension of Benson's outer approximation algorithm, and the second one is a dual variant of it. Both algorithms provide an inner as well as an outer approximation of the (upper and lower) images. Only one scalar convex program has to be solved in each iteration. We allow objective and constraint functions that are not necessarily differentiable, allow solid pointed polyhedral ordering cones, and relate the approximations to an appropriate -solution concept. Numerical examples are provided.
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