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In this paper, we propose a quasi Newton method to solve the robustcounterpart of an uncertain multiobjective optimization problem under anarbitrary finite uncertainty set. Here the robust counterpart of an uncertainmultiobjective optimization problem is the minimum of objective-wise worstcase, which is a nonsmooth deterministic multiobjective optimization problem.In order to solve this robust counterpart with the help of quasi Newton method,we construct a sub-problem using Hessian approximation and solve it todetermine a descent direction for the robust counterpart. We introduce anArmijo-type inexact line search technique to find an appropriate step length,and develop a modified BFGS formula to ensure positive definiteness of theHessian matrix at each iteration. By incorporating descent direction, steplength size, and modified BFGS formula, we write the quasi Newton's descentalgorithm for the robust counterpart. We prove the convergence of the algorithmunder standard assumptions and demonstrate that it achieves superlinearconvergence rate. Furthermore, we validate the algorithm by comparing it withthe weighted sum method through some numerical examples by using a performanceprofile.

A Quasi Newton Method for Uncertain Multiobjective Optimization Problems via Robust Optimization Approach