Speaker: Muhammad Umer, Bilkent University
Date & Time: April 1, 2022, Friday 13:30
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Title: Norm minimization-based convex vector optimization algorithms
Abstract: Our work is regarding a convex vector optimization problem (CVOP), which is the generalization of multiobjective optimization problem. We propose an algorithm to generate inner and outer polyhedral approximations to the set, called the upper image, of a bounded CVOP. It is an outer approximation algorithm and is based on solving norm-minimizing scalarizations. We also propose a modification of the algorithm by introducing an upper bound in order to limit the number of vertices considered, in each iteration, for evaluation. This helps in proving for the first time the finiteness of an algorithm for CVOPs. We also introduce a modification of norm minimizing scalarization using an additional constraint. Based on the modified scalarization, we propose a variant of the first algorithm which deals with a suitable compact subset of the upper image from the beginning. This leads to specify, for the first time, the convergence rate of an algorithm dealing with CVOPs.
The computational performance of the algorithms is illustrated using some of the benchmark test problems, which shows comparable results with respect to a CVOP algorithm, from the literature, that is based on Pascoletti-Serafini scalarization.
Bio: Muhammad Umer is a Ph.D. candidate in Industrial Engineering Department of Bilkent University. He received his B.E. and M.S. degrees in Aeronautical Engineering from National University of Sciences and Technology (NUST) and Air University from Pakistan in 2007 and 2013, respectively. His research interest includes vector optimization, multiobjective problems, set optimization and convex analysis.