A convex optimization approach for minimizing the ratio of indefinite quadratic functions over an ellipsoid
type: Item
instance of: scholarly article
title: A convex optimization approach for minimizing the ratio of indefinite quadratic functions over an ellipsoid
zbMATH Open document ID: 1176.90451
author: Amir Beck
author: Marc Teboulle
published in: Mathematical Programming. Series A. Series B
publication date: 2009-05-04T00:00:00Z
review text: The authors study a class of nonconvex optimization problems which possesses a hidden convexity property, that is, which can be shown to be equivalent to a convex problem and thus can be efficiently solved. The nonconvex minimization problem (RQ) considered in this paper involves an objective function which is the ratio of two nonconvex quadratic functions over a possibly degenerate ellipsoid. This formulation is a generalization of the so-called Regularized Total Least Squares problem (RTLS). This problem RQ can be recast as a semidefinite programming problem with no gap, and its global optimal solution can be extracted from the optimal solution of this semidefinite formulation. Then an extension of an iterative procedure used for the problem RTLS is proposed for solving the problem RQ. The corresponding algorithm is proven to be superlinearly convergent. Furthermore it produces an \(\epsilon\)-global solution after at most \(O(\sqrt{\ln\varepsilon^{-1}})\) iterations.
Mathematics Subject Classification ID: 90C22
Mathematics Subject Classification ID: 90C25
Mathematics Subject Classification ID: 62G05
zbMATH DE Number: 5550530
zbMATH Keywords: nonconvex quadratic minimization
zbMATH Keywords: strong duality
zbMATH Keywords: regularized total least squares
zbMATH Keywords: fixed point algorithms
zbMATH Keywords: convergence analysis
reviewed by: Jean-Jacques Strodiot
describes a project that uses: VanHuffel
MaRDI profile type: Publication
full work available at URL: s10107-007-0181-x
OpenAlex ID: W2057317983
cites work: Strong duality for a trust-region type relaxation of the quadratic assignment problem
cites work: On Lagrangian relaxation of quadratic matrix constraints
cites work: Q4779970
cites work: Quadratic Matrix Programming
cites work: Finding a Global Optimal Solution for a Quadratically Constrained Fractional Quadratic Problem with Applications to the Regularized Total Least Squares
cites work: Strong Duality in Nonconvex Quadratic Optimization with Two Quadratic Constraints
cites work: Lectures on modern convex optimization. Analysis, algorithms, and engineering applications
cites work: Hidden convexity in some nonconvex quadratically constrained quadratic programming
cites work: On Nonlinear Fractional Programming
cites work: The trust region subproblem and semidefinite programming*
cites work: Tikhonov Regularization and Total Least Squares
cites work: An Analysis of the Total Least Squares Problem
cites work: Q4530421
cites work: Q4001897
cites work: Q4324980
cites work: Convexity of quadratic transformations and its use in control and optimization
cites work: Efficient Algorithms for Solution of Regularized Total Least Squares
cites work: A semidefinite framework for trust region subproblems with applications to large scale minimization
cites work: Regularized total least squares based on quadratic eigenvalue problem solvers
cites work: Minimization of a Large-Scale Quadratic FunctionSubject to a Spherical Constraint
cites work: Indefinite Trust Region Subproblems and Nonsymmetric Eigenvalue Perturbations
cites work: New Results on Quadratic Minimization
DOI: 10.1007/S10107-007-0181-X
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description: scientific article; zbMATH DE number 5550530