On Local Non-Global Minimizers of Quadratic Optimization Problem with a Single Quadratic Constraint. (10th June 2020)

• Record Type: Journal Article
• Authors: Taati, Akram; Salahi, Maziar
• Is Part Of: Numerical functional analysis and optimization. Volume 41:Number 8(2020)
• Page Start: 969
• Page End: 1005
• Publication Date: 2020-06-10
• Subjects: Global optimization -- generalized eigenvalue problem -- local minimizer -- quadratically constrained quadratic optimization; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2020.1733605
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: In this paper, we consider the nonconvex quadratic optimization problem with a single quadratic constraint. First we give a theoretical characterization of the local non-global minimizers. Then we extend the recent characterization of the global minimizer via a generalized eigenvalue problem to the local non-global minimizers. Finally, we use these results to derive an efficient algorithm that finds the global minimizer of the problem with an additional linear inequality constraint.