Inexact Restoration approach for minimization with inexact evaluation of the objective function

A new method is introduced for minimizing a function that can be computed only inexactly, with different levels of accuracy. The challenge is to evaluate the (potentially very expensive) objective function with low accuracy as far as this does not interfere with the goal of getting high accuracy minimization at the end. For achieving this goal the problem is reformulated in terms of constrained optimization and handled with an Inexact Restoration technique. Convergence is proved and numerical experiments motivated by Electronic Structure Calculations are presented, which indicate that the new method overcomes current approaches for solving large-scale problems8517751791CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICO - CNPQFUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULO - FAPESP300933-2009-6; 400926-2013-02013/07375-0; 2006/53768-