SOLVING AN UNCERTAIN QUADRATIC MULTIOBJECTIVE OPTIMIZATION PROBLEM USING NEWTON’S DESCENT METHOD VIA A ROBUST OPTIMIZATION APPROACH

Abstract

In this paper, we develop a Newton’s descent method (NDM) for an uncertain quadratic multiobjective optimization problem (UQMOP). To accomplish this, we utilize a minimum of the objective wise worst case (OWWC) type robust counterpart (RC) of the UQMOP. The resulting RC is a nonsmooth multiobjective optimization problem (MOP). Our approach involves constructing a sub-problem to determine Newton’s descent direction (NDD) for the RC. An Armijo-type inexact line search (AILS) technique is employed to identify an appropriate step length. Using NDD and step length, we formulate a Newton’s descent algorithm (NDA) for the RC. Under some assumptions, we establish the convergence of NDA for the RC. Under specific assumptions, we demonstrate that the sequence defined by the NDA converges rapidly to the solution, exhibiting both superlinear and quadratic rate of convergence. Finally, we assess the efficacy of NDA by conducting a comparative analysis with the weighted sum method via various numerical problems. We obtain the non-dominated Pareto front for both methods, which support our method. © 2025 Journal of Applied and Numerical Optimization.