Derivative-free nonlinear optimization filter simplex

• Volume: 20, Issue: 4, page 679-688
• ISSN: 1641-876X

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Abstract

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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.

How to cite

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Aldina Correia, et al. "Derivative-free nonlinear optimization filter simplex." International Journal of Applied Mathematics and Computer Science 20.4 (2010): 679-688. <http://eudml.org/doc/208017>.

@article{AldinaCorreia2010,
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.},
author = {Aldina Correia, João Matias, Pedro Mestre, Carlos Serodio},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {nonlinear constrained optimization; filter methods; direct search methods},
language = {eng},
number = {4},
pages = {679-688},
title = {Derivative-free nonlinear optimization filter simplex},
url = {http://eudml.org/doc/208017},
volume = {20},
year = {2010},
}

TY - JOUR
AU - Aldina Correia
AU - João Matias
AU - Pedro Mestre
AU - Carlos Serodio
TI - Derivative-free nonlinear optimization filter simplex
JO - International Journal of Applied Mathematics and Computer Science
PY - 2010
VL - 20
IS - 4
SP - 679
EP - 688
AB - 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.
LA - eng
KW - nonlinear constrained optimization; filter methods; direct search methods
UR - http://eudml.org/doc/208017
ER -

References

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11. Correia, A., Matias, J., Mestre, P. and Serôdio, C. (2009). Derivative-free optimization and filter methods to solve nonlinear constrained problems, International Journal of Computer Mathematics 86(10): 1841-1851. Zbl1177.65085
12. Fletcher, R. and Leyffer, S. (2002). Nonlinear programming without a penalty function, Mathematical Programming. Series A 91(2): 239-269. Zbl1049.90088
13. Fletcher, R., Leyffer, S. and Toint, P. L. (2006). A brief history of filter method, Technical Report ANL/MCS-P1372-0906, Argonne National Laboratory, Mathematics and Computer Science Division, Argonne, IL.
14. Karas, E.W., Ribeiro, A.A., Sagastizábal, C. and Solodov, M. (2006). A bundle-filter method for nonsmooth convex constrained optimization, Mathematical Programming 1(116): 297-320. Zbl1165.90024
15. Nelder, J.A. and Mead, R. (1965). A simplex method for function minimization, The Computer Journal 7(4): 308-313. Zbl0229.65053

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