Exploiting band structure in unconstrained optimization without derivatives

Benoit Colson; Philippe Toint

Exploiting band structure in unconstrained optimization without derivatives

Research output: Contribution to journal › Article › peer-review

Abstract

This paper is concerned with derivative-free unconstrained optimization. We first discuss a method combining the use of interpolation polynomials and trust-region techniques to minimize a function whose derivatives are not available. We then show how the resulting algorithm may be adapted in a suitable way to consider problems for which the Hessian matrix is known to be sparse. Numerical experiments confirm the favourable behaviour of the method and in particular the advantages in terms of storage, function evaluations and speed.

Original language	English
Pages (from-to)	399-412
Number of pages	14
Journal	Optimization and Engineering
Issue number	2
Publication status	Published - 2001

Keywords

interpolation models
sparsity
trust-region methods
derivative-free optimization

1 Article

BFO, a trainable derivative-free Brute Force Optimizer for nonlinear bound-constrained optimization and equilibrium computations with continuous and discrete variables
Porcelli, M. & Toint, P., 30 Jun 2017, In: Transactions of the American Methematical Society. 44, 1, 28 p., 6.
Research output: Contribution to journal › Article › peer-review

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2 Active

DFO: Derivative free numerical algorithms for optimization
Toint, P. (PI), COLSON, B. (Researcher), Gratton, S. (PI), Tröltzsch, A. (Researcher) & RODRIGUES SAMPAIO, P. (CoI)
1/03/94 → …
Project: Research
ADALGOPT: ADALGOPT - Advanced algorithms in nonlinear optimization
Sartenaer, A. (CoI) & Toint, P. (CoI)
1/01/87 → …
Project: Research Axis

Trust-region algorithms for derivative-free optimization and nonlinear bilevel programming
Colson, B. (Author), Toint, P. (Supervisor), Henrard, J. (Jury), Sartenaer, A. (Jury), Savard, G. (Jury) & VICENTE, L. (Jury), 2003
Student thesis: Doc types › Doctor of Sciences

Cite this

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title = "Exploiting band structure in unconstrained optimization without derivatives",

abstract = "This paper is concerned with derivative-free unconstrained optimization. We first discuss a method combining the use of interpolation polynomials and trust-region techniques to minimize a function whose derivatives are not available. We then show how the resulting algorithm may be adapted in a suitable way to consider problems for which the Hessian matrix is known to be sparse. Numerical experiments confirm the favourable behaviour of the method and in particular the advantages in terms of storage, function evaluations and speed.",

keywords = " interpolation models, sparsity, trust-region methods, derivative-free optimization",

author = "Benoit Colson and Philippe Toint",

note = "Publication code : **RES. ACAD.",

year = "2001",

language = "English",

pages = "399--412",

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T1 - Exploiting band structure in unconstrained optimization without derivatives

AU - Colson, Benoit

AU - Toint, Philippe

N1 - Publication code : **RES. ACAD.

PY - 2001

Y1 - 2001

N2 - This paper is concerned with derivative-free unconstrained optimization. We first discuss a method combining the use of interpolation polynomials and trust-region techniques to minimize a function whose derivatives are not available. We then show how the resulting algorithm may be adapted in a suitable way to consider problems for which the Hessian matrix is known to be sparse. Numerical experiments confirm the favourable behaviour of the method and in particular the advantages in terms of storage, function evaluations and speed.

AB - This paper is concerned with derivative-free unconstrained optimization. We first discuss a method combining the use of interpolation polynomials and trust-region techniques to minimize a function whose derivatives are not available. We then show how the resulting algorithm may be adapted in a suitable way to consider problems for which the Hessian matrix is known to be sparse. Numerical experiments confirm the favourable behaviour of the method and in particular the advantages in terms of storage, function evaluations and speed.

KW - interpolation models

KW - sparsity

KW - trust-region methods

KW - derivative-free optimization

M3 - Article

SP - 399

EP - 412

JO - Optimization and Engineering

JF - Optimization and Engineering

IS - 2

ER -

Exploiting band structure in unconstrained optimization without derivatives

Abstract

Keywords

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Research output

BFO, a trainable derivative-free Brute Force Optimizer for nonlinear bound-constrained optimization and equilibrium computations with continuous and discrete variables

Projects

DFO: Derivative free numerical algorithms for optimization

ADALGOPT: ADALGOPT - Advanced algorithms in nonlinear optimization

Student theses

Trust-region algorithms for derivative-free optimization and nonlinear bilevel programming

Cite this