NDLI: A null-space primal-dual interior-point algorithm for nonlinear optimization with nice convergence properties

Content Provider	Springer Nature Link
Author	Liu, Xinwei Yuan, Yaxiang
Copyright Year	2009
Abstract	We present a null-space primal-dual interior-point algorithm for solving nonlinear optimization problems with general inequality and equality constraints. The algorithm approximately solves a sequence of equality constrained barrier subproblems by computing a range-space step and a null-space step in every iteration. The ℓ2 penalty function is taken as the merit function. Under very mild conditions on range-space steps and approximate Hessians, without assuming any regularity, it is proved that either every limit point of the iterate sequence is a Karush-Kuhn-Tucker point of the barrier subproblem and the penalty parameter remains bounded, or there exists a limit point that is either an infeasible stationary point of minimizing the ℓ 2 norm of violations of constraints of the original problem, or a Fritz-John point of the original problem. In addition, we analyze the local convergence properties of the algorithm, and prove that by suitably controlling the exactness of range-space steps and selecting the barrier parameter and Hessian approximation, the algorithm generates a superlinearly or quadratically convergent step. The conditions on guaranteeing that all slack variables are still positive for a full step are presented.
Ending Page	193
Page Count	31
Starting Page	163
File Format	PDF
ISSN	00255610
e-ISSN	14364646
Journal	Mathematical Programming
Issue Number	1
Volume Number	125
Language	English
Publisher	Springer-Verlag
Publisher Date	2009-03-03
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Theoretical, Mathematical and Computational Physics Nonlinear optimization with inequality and equality constraints Null-space technique Interior-point methods Mathematical Methods in Physics Mathematics of Computing Calculus of Variations and Optimal Control; Optimization Global and local convergences Numerical Analysis Mathematical programming methods Nonlinear programming Combinatorics Primal-dual interior-point methods
Content Type	Text
Resource Type	Article
Subject	Mathematics Software

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