Newton Iteration with Weighted Exponential Penalty Function for Solving Multi-Objective Constrained Optimization Problems

Abstract

In this paper, the Newton iterative method and weighted exponential penalty function method for solving multi-objective constrained optimization problems are proposed on the basis of classical optimization methods for mathematical planning. Firstly, according to the characteristics of the objective function, it is transformed into a single-objective constrained optimization problem using variable weight coefficients. Then according to the characteristics of the constraints, the exponential penalty function method is used to transform it into an unconstrained optimization problem. Finally, Newton's method is used to solve the transformed unconstrained optimization problem to obtain the efficient Pareto solution of the original problem. The convergence of the method is included in the paper, and numerical experiments show that our proposed method can obtain a set of effective Pareto solutions corresponding to multi-objective optimization problems in different dimensions.