Delayed Weighted Gradient Method with simultaneous step-sizes for strongly convex optimization

The Delayed Weighted Gradient Method (DWGM) is a two-step gradient algorithm that is efficient for the minimization of large scale strictly convex quadratic functions. It has orthogonality properties that make it to compete with the Conjugate Gradient (CG) method. Both methods calculate in sequence...

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Bibliographic Details
Published in:Computational optimization and applications Vol. 89; no. 1; pp. 151 - 182
Main Authors: Lara, Hugo, Aleixo, Rafael, Oviedo, Harry
Format: Journal Article
Language:English
Published: New York Springer US 01.09.2024
Springer Nature B.V
Subjects:
Algorithms
Conjugate gradient method
Convex analysis
Convex and Discrete Geometry
Convexity
Management Science
Mathematics
Mathematics and Statistics
Methods
Operations Research
Operations Research/Decision Theory
Optimization
Orthogonality
Quadratic equations
Statistics
Two dimensional analysis
Gradient methods
Strongly convex functions
Conjugate gradient methods
Large-scale optimization
ISSN:0926-6003, 1573-2894
Online Access:Get full text
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Summary:The Delayed Weighted Gradient Method (DWGM) is a two-step gradient algorithm that is efficient for the minimization of large scale strictly convex quadratic functions. It has orthogonality properties that make it to compete with the Conjugate Gradient (CG) method. Both methods calculate in sequence two step-sizes, CG minimizes the objective function and DWGM the gradient norm, alongside two search directions defined over first order current and previous iteration information. The objective of this work is to accelerate the recently developed extension of DWGM to nonquadratic strongly convex minimization problems. Our idea is to define the step-sizes of DWGM in a unique two dimensional convex quadratic optimization problem, calculating them simultaneously. Convergence of the resulting algorithm is analyzed. Comparative numerical experiments illustrate the effectiveness of our approach.
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ISSN:0926-6003
1573-2894
DOI:10.1007/s10589-024-00586-4