Please use this identifier to cite or link to this item: https://doi.org/10.3934/jimo.2018190
Title: A primal-dual interior-point method capable of rapidly detecting infeasibility for nonlinear programs
Authors: Dai, Y.-H.
Liu, X.-W.
Sun, J. 
Keywords: Constrained optimization
Global and local convergence
Infeasibility
Interior-point method
Nonlinear programming
Issue Date: 2020
Publisher: American Institute of Mathematical Sciences
Citation: Dai, Y.-H., Liu, X.-W., Sun, J. (2020). A primal-dual interior-point method capable of rapidly detecting infeasibility for nonlinear programs. Journal of Industrial and Management Optimization 16 (2) : 1009-1035. ScholarBank@NUS Repository. https://doi.org/10.3934/jimo.2018190
Rights: Attribution 4.0 International
Abstract: With the help of a logarithmic barrier augmented Lagrangian function, we can obtain closed-form solutions of slack variables of logarithmicbarrier problems of nonlinear programs. As a result, a two-parameter primaldual nonlinear system is proposed, which corresponds to the Karush-Kuhn-Tucker point and the infeasible stationary point of nonlinear programs, respectively, as one of two parameters vanishes. Based on this distinctive system, we present a primal-dual interior-point method capable of rapidly detecting infeasibility of nonlinear programs. The method generates interior-point iterates without truncation of the step. It is proved that our method converges to a Karush-Kuhn-Tucker point of the original problem as the barrier parameter tends to zero. Otherwise, the scaling parameter tends to zero, and the method converges to either an infeasible stationary point or a singular stationary point of the original problem. Moreover, our method has the capability to rapidly detect the infeasibility of the problem. Under suitable conditions, the method can be superlinearly or quadratically convergent to the Karush-Kuhn-Tucker point if the original problem is feasible, and it can be superlinearly or quadratically convergent to the infeasible stationary point when the problem is infeasible. Preliminary numerical results show that the method is ecient in solving some simple but hard problems, where the superlinear convergence to an infeasible stationary point is demonstrated when we solve two infeasible problems in the literature. © 2020, American Institute of Mathematical Sciences.
Source Title: Journal of Industrial and Management Optimization
URI: https://scholarbank.nus.edu.sg/handle/10635/196192
ISSN: 1547-5816
DOI: 10.3934/jimo.2018190
Rights: Attribution 4.0 International
Appears in Collections:Elements
Staff Publications

Show full item record
Files in This Item:
File Description SizeFormatAccess SettingsVersion 
10_3934_jimo_2018190.pdf614.72 kBAdobe PDF

OPEN

NoneView/Download

SCOPUSTM   
Citations

1
checked on Nov 28, 2021

Page view(s)

20
checked on Dec 2, 2021

Google ScholarTM

Check

Altmetric


This item is licensed under a Creative Commons License Creative Commons