New advances in inexact restoration methods to cover new applications

Abstract

In this project, we present some research alternatives related to Inexact Restoration methods so that it is possible to use them efficiently to address some interesting applications. We propose to do a modular presentation of the algorithms so that any modification alternative can be made without the entire theory needing to be revised. In this way, we believe that several acceleration elements can be considered for each specific problem to be solved. With this philosophy, we intend to deal with problems arising from Data Science and Structural Optimization. In the first case, we hope to solve constrained optimization problems, in which is convenient the imprecise evaluation of the functions that define it. For this, we will use an artificial variable and an artificial constraint to control the level of precision in evaluating the functions involved and treat them in an Inexact Restoration scheme. For Structural Optimization, we intend to present a globalization of a Sequential Linear Programming method using the developed Inexact Restoration theory and allowing specific accelerations with respect to the problem of interest. (AU)