<abstract xml:lang="en" xmlns="http://www.w3.org/1999/xhtml"><p>The filter method is a technique for solving nonlinear programming problems. The filter algorithm has two phases in each iteration. The first one reduces a measure of infeasibility, while in the second the objective function value is reduced. In real optimization problems, usually the objective function is not differentiable or its derivatives are unknown. In these cases it becomes essential to use optimization methods where the calculation of the derivatives or the verification of their existence is not necessary: direct search methods or derivative-free methods are examples of such techniques. In this work we present a new direct search method, based on simplex methods, for general constrained optimization that combines the features of simplex and filter methods. This method neither computes nor approximates derivatives, penalty constants or Lagrange multipliers.</p></abstract>

The filter method is a technique for solving nonlinear programming problems. The filter algorithm has two phases in each iteration. The first one reduces a measure of infeasibility, while in the second the objective function value is reduced. In real optimization problems, usually the objective function is not differentiable or its derivatives are unknown. In these cases it becomes essential to use optimization methods where the calculation of the derivatives or the verification of their existence is not necessary: direct search methods or derivative-free methods are examples of such techniques. In this work we present a new direct search method, based on simplex methods, for general constrained optimization that combines the features of simplex and filter methods. This method neither computes nor approximates derivatives, penalty constants or Lagrange multipliers.

Derivative-free nonlinear optimization filter simplex

ESTGF-IPP, School of Technology and Management of Felgueiras, Polytechnic Institute of Porto, 4610-156 Felgueiras, Portugal

CM-UTAD, Centre for Mathematics, University of Trás-os-Montes and Alto Douro, 5000-911 Vila Real, Portugal

CITAB, Centre for the Research and Technology of Agro-Environment and Biological Sciences, University of Trás-os-Montes and Alto Douro, 5000-911 Vila Real, Portugal

International Journal of Applied Mathematics and Computer Science

{"article-title":"Derivative-free nonlinear optimization filter simplex"}

The filter method is a technique for solving nonlinear programming problems. The filter algorithm has two phases in each iteration. The first one reduces a...

Derivative-free nonlinear optimization filter simplex

Published Online: Dec 20, 2010

Page range: 679 - 688

DOI: https://doi.org/10.2478/v10006-010-0051-1

Keywords
nonlinear constrained optimization, filter methods, direct search methods

This content is open access.

Derivative-free nonlinear optimization filter simplex

Published Online: Dec 20, 2010

Page range: 679 - 688

DOI: https://doi.org/10.2478/v10006-010-0051-1

Keywordsnonlinear constrained optimization, filter methods, direct search methods

This content is open access.

Keywords
nonlinear constrained optimization, filter methods, direct search methods