Economic inexact restoration for derivative-free expensive function minimization and applications

The Inexact Restoration approach has proved to be an adequate tool for handling the problem of minimizing an expensive function within an arbitrary feasible set by using different degrees of precision in the objective function. The Inexact Restoration framework allows one to obtain suitable convergence and complexity results for an approach that rationally combines low- and high-precision evaluations. In the present research, it is recognized that many problems with expensive objective functions are nonsmooth and, sometimes, even discontinuous. Having this in mind, the Inexact Restoration approach is extended to the nonsmooth or discontinuous case. Although optimization phases that rely on smoothness cannot be used in this case, basic convergence and complexity results are recovered. A derivative-free optimization phase is defined and the subproblems that arise at this phase are solved using a regularization approach that take advantage of different notions of stationarity. The new methodology is applied to the problem of reproducing a controlled experiment that mimics the failure of a dam

Inexact Restoration Approach For Minimization With Inexact Evaluation Of The Objective Function

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)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 problems.8517751791Serbian Ministry of Education, Science, and Technological Development [174030]FAPESP (Fundacao de Amparo a Pesquisa do Estado de Sao Paulo under projects CEPID-Cemeai on Industrial Mathematics) [2013/07375-0, PT 2006/53768-0]CNPq [300933-2009-6, 400926-2013-0]Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq

Inexact Restoration Approach For Minimization With Inexact Evaluation Of The Objective Function

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)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 problems.8530017751791Serbian Ministry of Education, Science, and Technological Development [174030]FAPESP (Fundacao de Amparo a Pesquisa do Estado de Sao Paulo under projects CEPID-Cemeai on Industrial Mathematics) [2013/07375-0, PT 2006/53768-0]CNPq [300933-2009-6, 400926-2013-0]Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq

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-