NDLI: An interior-point trust-funnel algorithm for nonlinear optimization

Content Provider	Springer Nature Link
Author	Curtis, Frank E. Gould, Nicholas I. M. Robinson, Daniel P. Toint, Philippe L.
Copyright Year	2016
Abstract	We present an interior-point trust-funnel algorithm for solving large-scale nonlinear optimization problems. The method is based on an approach proposed by Gould and Toint (Math Prog 122(1):155–196, 2010) that focused on solving equality constrained problems. Our method is similar in that it achieves global convergence guarantees by combining a trust-region methodology with a funnel mechanism, but has the additional capability of being able to solve problems with both equality and inequality constraints. The prominent features of our algorithm are that (i) the subproblems that define each search direction may be solved with matrix-free methods so that derivative matrices need not be formed or factorized so long as matrix-vector products with them can be performed; (ii) the subproblems may be solved approximately in all iterations; (iii) in certain situations, the computed search directions represent inexact sequential quadratic optimization steps, which may be desirable for fast local convergence; (iv) criticality measures for feasibility and optimality aid in determining whether only a subset of computations need to be performed during a given iteration; and (v) no merit function or filter is needed to ensure global convergence.
Ending Page	134
Page Count	62
Starting Page	73
File Format	PDF
ISSN	00255610
e-ISSN	14364646
Journal	Mathematical Programming
Issue Number	1-2
Volume Number	161
Language	English
Publisher	Springer Berlin Heidelberg
Publisher Date	2016-04-07
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Theoretical, Mathematical and Computational Physics Nonlinear optimization Funnel mechanism Trust-region methods Constrained optimization Barrier-SQP methods Mathematical Methods in Physics Nonsmooth analysis Calculus of Variations and Optimal Control; Optimization Mathematics of Computing Numerical Analysis Mathematical programming methods Methods of successive quadratic programming type Nonconvex programming, global optimization Large-scale optimization Nonlinear programming Combinatorics Methods of nonlinear programming type Ill-posedness, regularization
Content Type	Text
Resource Type	Article
Subject	Mathematics Software

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1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
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