NDLI: Interior-point ℓ2-penalty methods for nonlinear programming with strong global convergence properties

Content Provider	Springer Nature Link
Author	Goldfarb, D. Chen, L.
Copyright Year	2006
Abstract	We propose two line search primal-dual interior-point methods for nonlinear programming that approximately solve a sequence of equality constrained barrier subproblems. To solve each subproblem, our methods apply a modified Newton method and use an ℓ2-exact penalty function to attain feasibility. Our methods have strong global convergence properties under standard assumptions. Specifically, if the penalty parameter remains bounded, any limit point of the iterate sequence is either a Karush-Kuhn-Tucker (KKT) point of the barrier subproblem, or a Fritz-John (FJ) point of the original problem that fails to satisfy the Mangasarian-Fromovitz constraint qualification (MFCQ); if the penalty parameter tends to infinity, there is a limit point that is either an infeasible FJ point of the inequality constrained feasibility problem (an infeasible stationary point of the infeasibility measure if slack variables are added) or a FJ point of the original problem at which the MFCQ fails to hold. Numerical results are given that illustrate these outcomes.
Ending Page	36
Page Count	36
Starting Page	1
File Format	PDF
ISSN	00255610
e-ISSN	14364646
Journal	Mathematical Programming
Issue Number	1
Volume Number	108
Language	English
Publisher	Springer-Verlag
Publisher Date	2006-02-02
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	modified Newton method penalty-barrier method nonlinear programming global convergence Mathematical and Computational Physics Direct methods for linear systems and matrix inversion Optimization Constrained optimization primal-dual interior-point method Mathematical Methods in Physics Mathematics of Computing Numerical Analysis Mathematical programming methods Calculus of Variations and Optimal Control Nonlinear programming Combinatorics Methods of nonlinear programming type
Content Type	Text
Resource Type	Article
Subject	Mathematics Software

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