Solving structured nonlinear least-squares and nonlinear feasibility problems with expensive functions

Markus Kaiser, Kathrin Klamroth, Alexander Thekale, Philippe Toint

Résultats de recherche: Livre/Rapport/RevueAutre rapport

Résumé

We present an algorithm for nonlinear least-squares and nonlinear feasibility problems, i.e. for systems of nonlinear equations and nonlinear inequalities, which depend on the outcome of expensive functions for which derivatives are assumed to be unavailable. Our algorithm combines derivative-free techniques with filter trust-region methods to keep the number of expensive function evaluations low and to obtain a robust method. Under adequate assumptions, we show global convergence to a feasible point. Numerical results indicate a significant reduction in function evaluations compared to other derivative based and derivative-free solvers for nonlinear feasibility problems.
langue originaleAnglais
Lieu de publicationNamur
EditeurFUNDP. Namur center for complex systems
Volume10(7)
étatPublié - 2010

Série de publications

NomNAXYS Technical Report
EditeurDepartment of Mathematics, University of Namur
Volume07-2010

Empreinte digitale

Nonlinear Least Squares
Derivative-free
Evaluation Function
Derivative
Trust Region Method
Filter Method
System of Nonlinear Equations
Robust Methods
Global Convergence
Numerical Results

Citer ceci

Kaiser, M., Klamroth, K., Thekale, A., & Toint, P. (2010). Solving structured nonlinear least-squares and nonlinear feasibility problems with expensive functions. (NAXYS Technical Report; Vol 07-2010). Namur: FUNDP. Namur center for complex systems.
Kaiser, Markus ; Klamroth, Kathrin ; Thekale, Alexander ; Toint, Philippe. / Solving structured nonlinear least-squares and nonlinear feasibility problems with expensive functions. Namur : FUNDP. Namur center for complex systems, 2010. (NAXYS Technical Report).
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abstract = "We present an algorithm for nonlinear least-squares and nonlinear feasibility problems, i.e. for systems of nonlinear equations and nonlinear inequalities, which depend on the outcome of expensive functions for which derivatives are assumed to be unavailable. Our algorithm combines derivative-free techniques with filter trust-region methods to keep the number of expensive function evaluations low and to obtain a robust method. Under adequate assumptions, we show global convergence to a feasible point. Numerical results indicate a significant reduction in function evaluations compared to other derivative based and derivative-free solvers for nonlinear feasibility problems.",
keywords = "derivative-free, feasibility problem, structured problems, global convergence. , trust-region, nonlinear least-squares, nonlinear systems, multidimensional filter",
author = "Markus Kaiser and Kathrin Klamroth and Alexander Thekale and Philippe Toint",
year = "2010",
language = "English",
volume = "10(7)",
series = "NAXYS Technical Report",
publisher = "FUNDP. Namur center for complex systems",

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Kaiser, M, Klamroth, K, Thekale, A & Toint, P 2010, Solving structured nonlinear least-squares and nonlinear feasibility problems with expensive functions. NAXYS Technical Report, VOL. 07-2010, VOL. 10(7), FUNDP. Namur center for complex systems, Namur.

Solving structured nonlinear least-squares and nonlinear feasibility problems with expensive functions. / Kaiser, Markus; Klamroth, Kathrin; Thekale, Alexander; Toint, Philippe.

Namur : FUNDP. Namur center for complex systems, 2010. (NAXYS Technical Report; Vol 07-2010).

Résultats de recherche: Livre/Rapport/RevueAutre rapport

TY - BOOK

T1 - Solving structured nonlinear least-squares and nonlinear feasibility problems with expensive functions

AU - Kaiser, Markus

AU - Klamroth, Kathrin

AU - Thekale, Alexander

AU - Toint, Philippe

PY - 2010

Y1 - 2010

N2 - We present an algorithm for nonlinear least-squares and nonlinear feasibility problems, i.e. for systems of nonlinear equations and nonlinear inequalities, which depend on the outcome of expensive functions for which derivatives are assumed to be unavailable. Our algorithm combines derivative-free techniques with filter trust-region methods to keep the number of expensive function evaluations low and to obtain a robust method. Under adequate assumptions, we show global convergence to a feasible point. Numerical results indicate a significant reduction in function evaluations compared to other derivative based and derivative-free solvers for nonlinear feasibility problems.

AB - We present an algorithm for nonlinear least-squares and nonlinear feasibility problems, i.e. for systems of nonlinear equations and nonlinear inequalities, which depend on the outcome of expensive functions for which derivatives are assumed to be unavailable. Our algorithm combines derivative-free techniques with filter trust-region methods to keep the number of expensive function evaluations low and to obtain a robust method. Under adequate assumptions, we show global convergence to a feasible point. Numerical results indicate a significant reduction in function evaluations compared to other derivative based and derivative-free solvers for nonlinear feasibility problems.

KW - derivative-free

KW - feasibility problem

KW - structured problems

KW - global convergence.

KW - trust-region

KW - nonlinear least-squares

KW - nonlinear systems

KW - multidimensional filter

M3 - Other report

VL - 10(7)

T3 - NAXYS Technical Report

BT - Solving structured nonlinear least-squares and nonlinear feasibility problems with expensive functions

PB - FUNDP. Namur center for complex systems

CY - Namur

ER -

Kaiser M, Klamroth K, Thekale A, Toint P. Solving structured nonlinear least-squares and nonlinear feasibility problems with expensive functions. Namur: FUNDP. Namur center for complex systems, 2010. (NAXYS Technical Report).