An inexact restoration approach to optimization problems with multiobjective constraints under weighted-sum scalarization

We apply a flexible Inexact-Restoration (IR) algorithm to optimization problems with multiobjective constraints under the weighted-sum scalarization approach. In IR methods each iteration has two phases. In the first phase one aims to improve the feasibility and, in the second phase, one minimizes a suitable objective function. We show that with the IR framework there is a natural way to explore the structure of the problem in both IR phases. Numerical experiments are conducted on Portfolio optimization, the Moré-Garbow-Hillstrom collection, and random fourth-degree polynomials, where we show the advantages of exploiting the structure of the problem.