Polynomial Multi-objective Optimization with Applications

Abstract: 

This is a final presentation of an Honours research project supervised by Guoyin Li.

Multi-objective optimization is an area of multiple criteria decision making which concerned with mathematical optimization problems involving more than one objective function to be optimized simultaneously. In 2012, V.Blanco and J.Puerto proposed a semi-definite programming (SDP) approximation scheme for solving a multi-objective linear programming problem. As an extension, we examine the polynomial multi-objective optimization problems (PMOPs). Our main motivation comes from the mean-variance cardinality constrained portfolio optimization problems which can be equivalently reformulated as PMOPs. In this talk, we will first present a weighted-sum method which reduces a PMOP into a single-objective nonconvex polynomial optimization problem. The solutions of the single-objective problems forms a subset of the weakly Pareto solutions of the underlying PMOPs. We then solve the single-objective optimization problems via SDP techniques.  At last, we will present some preliminary numerical simulation of the method by applying it to the mean variance cardinality constrained portfolio problem.