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How the Augmented Lagrangian Algorithm Can Deal with an Infeasible Convex Quadratic Optimization Problem

Year: 2016

Type: article

Abstract: This paper analyses the behavior of the augmented Lagrangian algorithm when it deals with an infeasible convex quadratic optimization problem. It is shown that the algorithm finds a point that, on the one hand, satisfies the constraints shifted by the smallest possible shift that makes them feasible and, on the other hand, minimizes the objective on the corresponding shifted constrained set. The speed of convergence to such a point is globally linear, with a rate that is inversely proportional to the augmentation parameter. This suggests us a rule for determining the augmentation parameter that aims at controlling the speed of convergence of the shifted constraint norm to zero; this rule has the advantage of generating bounded augmentation parameters even when the problem is infeasible.

Source: Journal of convex analysis

DOI: 10.68381/jca23016

Authors: Alice Chiche, Jean Charles Gilbert

Institutions: Institut national de recherche en sciences et technologies du numérique, Artelys (France), Électricité de France (France)

Language: English

Topic: Advanced Optimization Algorithms Research

Subfield: Numerical Analysis

Field: Mathematics

Domain: Physical Sciences

Open Access status: bronze

Funder: Association Nationale de la Recherche et de la Technologie

OpenAlex ID: W2339880967