Inexact Restoration for Minimization with Inexact Evaluation both of the Objective Function and the Constraints

TL;DR

This paper combines two Inexact Restoration methods to address constrained optimization problems with errors in evaluating the objective, constraints, and derivatives, providing new complexity and convergence results.

Contribution

It introduces a unified Inexact Restoration approach for problems with inexact evaluations of objectives, constraints, and derivatives, along with theoretical analysis.

Findings

Method achieves convergence despite evaluation errors

Complexity bounds are established for the combined approach

Theoretical results demonstrate robustness to inexact data

Abstract

In a recent paper an Inexact Restoration method for solving continuous constrained optimization problems was analyzed from the point of view of worst-case functional complexity and convergence. On the other hand, the Inexact Restoration methodology was employed, in a different research,to handle minimization problems with inexact evaluation and simple constraints. These two methodologies are combined in the present report, for constrained minimization problems in which both the objective function and the constraints, as well as their derivatives, are subject to evaluation errors. Together with a complete description of the method, complexity and convergence results will be proved.