Rapid infeasibility detection in a mixed logarithmic barrier-augmented Lagrangian method for nonlinear optimization. (3rd September 2019)

• Record Type: Journal Article
• Authors: Armand, Paul; Tran, Ngoc Nguyen
• Is Part Of: Optimization methods and software. Volume 34:Number 5(2019)
• Page Start: 991
• Page End: 1013
• Publication Date: 2019-09-03
• Subjects: Infeasibility detection -- nonlinear optimization -- primal-dual methods -- interior-point method -- augmented Lagrangian method; 49M15 -- 65K05 -- 90C06 -- 90C30 -- 90C51; Mathematical optimization -- Periodicals; Algorithms -- Periodicals; 519.7
• DOI: 10.1080/10556788.2018.1528250
• Languages: English
• ISSNs: 1055-6788

Abstract

ABSTRACT: We present a modification of a primal-dual algorithm based on a mixed augmented Lagrangian and a log-barrier penalty function. The goal of this new feature is to quickly detect infeasibility. An additional parameter is introduced to balance the minimization of the objective function and the realization of the constraints. The global convergence of the modified algorithm is analysed under mild assumptions. We also show that under a suitable choice of the parameters along the iterations, the rate of convergence of the algorithm to an infeasible stationary point is superlinear. This is the first local convergence result for the class of interior point methods in the infeasible case. We finally report some numerical experiments to show that this new algorithm is quite efficient to detect infeasibility and does not deteriorate the overall behavior in the general case.