A PRIMAL-DUAL INTERIOR-POINT TECHNIQUE TO SOLVE MULTI-OBJECTIVE OPTIMIZATION PROBLEMS WITH AN APPLICATION TO OPTIMAL CONTROL PROBLEM

This paper introduces a primal-dual interior-point technique to determine the Pareto optimal solution for multi-objective optimization problems (MOPs). A direction-based approach is utilized to transform MOPs into a set of single-objective optimization subproblems. Then, the subproblems are solved by using a primal-dual interior-point method (PD-IPM). The PD-IPM utilizes the Newton method to calculate the primal-dual direction at each step to solve the perturbed Karush-Kuhn-Tucker optimality conditions. A merit function is introduced to take the suitable step lengths along the search directions. To demonstrate the efficiency of the proposed method, we applied it to some constrained test problems. As an application, we use proposed algorithm to an optimal control problem of carbon dioxide emission from energy sector, which aims to derive a mathematical framework to effectively utilize the available mitigation options to curtail CO2 emission from energy use. We propose a multi-objective approach to find the optimal mitigation strategies to minimize the CO2 level from energy sector as well as to minimize the cost of implementation of mitigation strategies.