Primal and Dual Approximation Algorithms for Convex Vector Optimization Problems
Vector optimization problems can be seen as extensions of multi- objective optimization problems where the partial order on the objective space is induced by a polyhedral ordering cone C. We provide two approximation algorithms for solving convex vector optimization problems (CVOPs). The algorithms work for any number of objectives and they 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, and relate the approximations to an appropriate ε- solution concept. A current research direction involves the convergence analysis of the algorithms and the extensions to solve the unbounded CVOPs.
Bio: Firdevs Ulus is an Assistant Professor in the Department of Industrial Engineering at Bilkent University. She got her PhD degree in Operations Research and Financial Engineering at Princeton University; MS degree in Mathematics at Sabancı University; and Bachelor’s degree in Manufacturing Systems (Industrial) Engineering with minor degree in Mathematics also at Sabancı University. She is working on vector (multi-objective) optimization problems, algorithms and applications in financial mathematics and economics.