A TRUST-REGION INTERIOR-POINT TECHNIQUE TO SOLVE MULTI-OBJECTIVE OPTIMIZATION PROBLEMS AND ITS APPLICATION TO A TUBERCULOSIS OPTIMAL CONTROL PROBLEM

Abstract

We introduce a trust-region interior-point technique to generate the Pareto optimal solution for multi-objective optimization problems. The Pascoletti-Serafini scalarization technique is utilized to convert a multi-objective optimization problem into a set of single-objective optimization subproblems. Then, the subproblems are solved by a trust-region interior-point method. Using the sequential quadratic programming technique, the algorithm proceeds through a sequence of barrier problems. With the help of the stationary points of a merit function, we obtain stationary points of the objective function of the barrier problem. It is shown that the directions that are used to find the sequence of iterates of the proposed method are descent direction of the used merit function. To show the efficiency of the proposed method, we show its performance on some standard test problems. As an application, we apply the proposed algorithm to solve an optimal control problem for a tuberculosis model. The model problem is a minimization problem and it has two objectives: one is the sum of the active infections patient and persistent latent individual, and the other is the cost to implement the control strategies.