A derivative-free trust-funnel method for equality-constrained nonlinear optimization

Research output: Contribution to journalArticle

Abstract

Abstract: A new derivative-free method is proposed for solving equality-constrained nonlinear optimization problems. This method is of the trust-funnel variety and is also based on the use of polynomial interpolation models. In addition, it uses a self-correcting geometry procedure in order to ensure that the interpolation problem is well defined in the sense that the geometry of the set of interpolation points does not differ too much from the ideal one. The algorithm is described in detail and some encouraging numerical results are presented.

Graphical Abstract: [Figure not available: see fulltext.]

Original languageEnglish
Pages (from-to)25-49
Number of pages25
JournalComputational Optimization and Applications
Volume61
Issue number1
DOIs
Publication statusPublished - 1 May 2015

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Derivative-free
Constrained Optimization
Nonlinear Optimization
Interpolation
Equality
Derivative-free Methods
Derivatives
Polynomial Interpolation
Interpolation Problem
Nonlinear Problem
Well-defined
Figure
Geometry
Interpolate
Optimization Problem
Numerical Results
Polynomials
Model
Graphics

Keywords

  • Derivative-free optimization
  • Equality constraints
  • Trust funnel
  • Trust-region method

Cite this

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abstract = "Abstract: A new derivative-free method is proposed for solving equality-constrained nonlinear optimization problems. This method is of the trust-funnel variety and is also based on the use of polynomial interpolation models. In addition, it uses a self-correcting geometry procedure in order to ensure that the interpolation problem is well defined in the sense that the geometry of the set of interpolation points does not differ too much from the ideal one. The algorithm is described in detail and some encouraging numerical results are presented.Graphical Abstract: [Figure not available: see fulltext.]",
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N2 - Abstract: A new derivative-free method is proposed for solving equality-constrained nonlinear optimization problems. This method is of the trust-funnel variety and is also based on the use of polynomial interpolation models. In addition, it uses a self-correcting geometry procedure in order to ensure that the interpolation problem is well defined in the sense that the geometry of the set of interpolation points does not differ too much from the ideal one. The algorithm is described in detail and some encouraging numerical results are presented.Graphical Abstract: [Figure not available: see fulltext.]

AB - Abstract: A new derivative-free method is proposed for solving equality-constrained nonlinear optimization problems. This method is of the trust-funnel variety and is also based on the use of polynomial interpolation models. In addition, it uses a self-correcting geometry procedure in order to ensure that the interpolation problem is well defined in the sense that the geometry of the set of interpolation points does not differ too much from the ideal one. The algorithm is described in detail and some encouraging numerical results are presented.Graphical Abstract: [Figure not available: see fulltext.]

KW - Derivative-free optimization

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KW - Trust funnel

KW - Trust-region method

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