EUROPT 2025
Abstract Submission

33. Hybrid scalarization for multi-objective semi definite polynomial optimization

Invited abstract in session MD-11: Applications of conic optimization, stream Conic Optimization.

Monday, 16:30-18:30
Room: B100/5017

Authors (first author is the speaker)

1. SUJEET KUMAR SINGH
OPERATIONS RESEARCH, INDIAN STATISTICAL INSTITUTE

Abstract

Decision making is part of our lives, and almost all decision problems have conflicting criteria for evaluation. Such problems are referred to as multiobjective optimization problems (MOOPs). We intend to develop new scalarization techniques using a modified goal function for the MOOP. Although multiobjective optimization problems have a rich literature on scalarizing methods, the existing weighing scalarization methods have some deficiencies in assigning the weights and then finding the solution per the objectives’ priority to tackle the incommensurability in heterogeneous objectives. Further, the weighing methods are unable to generate the Pareto points, which fall on the nonconvex part of the Pareto front. We
consider these issues and propose the Gamma-connective scalarization technique to solve the multi-objective optimization problem. The underline functions are considered to be the higher-degree polynomials and the recently developed sum of squares(SOS) techniques is used for equivalent PSD conversion. Positive semidefinite (PSD) optimization has efficient tools like YALMIP and SOSTOOLS to work with efficiently. These tools make PSD a tractable convex optimization problem. The performance of the proposed method would be evaluated using some measure of closeness to the ideal solution for several test problems.

Keywords

Status: accepted

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