A Newton-Type Globally Convergent Interior-Point Method to Solve Multi-Objective Optimization Problems (Journal of Computational Mathematics, 2023)
This paper proposes an interior-point technique for detecting the nondominated pointsof multi-objective optimization problems using the direction-based cone method. Conemethod decomposes the multi-objective optimization problems into a set of single-objectiveoptimization problems. For this set of problems, parametric perturbed KKT conditionsare derived. Subsequently, an interior point technique is developed to solve the parametricperturbed KKT conditions. A differentiable merit function is also proposed whose stationary point satisfies the KKT conditions. Under some mild assumptions, the proposedalgorithm is shown to be globally convergent. Numerical results of unconstrained and constrained multi-objective optimization test problems are presented. Also, three performancemetrics (modified generational distance, hypervolume, inverted generational distance) areused on some test problems to investigate the efficiency of the proposed algorithm. Wealso compare the results of the proposed algorithm with the results of some other existingpopular methods.