A Newton-Based Perturbation Method For A Robust Inverse Optimization Problem

In this paper, we focus on studying an inverse robust linear programming problem, in which the parameters in both the objective function and the robust constraint set need to be adjusted as little as possible so that a known feasible solution becomes the optimal one. We formulate this inverse problem as a optimization problem with a linear equality constraint, a second-order cone complementarity constraint and a linear complementarity constraint. We use a perturbation approach to solve the inverse problem. An inexact Newton method with Armijo line search is applied to solve the perturbed problem. Finally, the numerical result is reported to show the effectiveness of the approach.