NEWTON'S METHOD FOR UNCERTAIN MULTIOBJECTIVE OPTIMIZATION PROBLEMS UNDER FINITE UNCERTAINTY SETS

Abstract

In this paper, we develop Newton's method for robust counterpart of an uncertain multiobjective optimization problem under an arbitrary finite uncertainty nonempty set. Here the robust counterpart of an uncertain multiobjective optimization problem is the minimum of objective wise worst case, which is the nonsmooth deterministic multiobjective optimization problem. To solve this robust counterpart with the help of Newton's method, a suproblem is constructed and solved to find a descent direction for robust counterpart. An Armijo type inexact line search technique is developed to find a suitable step length. With the help of the descent direction and step length, we present the Newton's algorithm for the robust counterpart. The convergence of the Newton's algorithm for the robust counterpart is obtained under some usual assumptions. We also prove that the algorithm converges with super linear and quadratic rate under different assumptions. Finally, we verify the algorithm and compare with the weighted sum method via some numerical problems.