On convergence of a q-random coordinate constrained algorithm for non-convex problems

We propose a random coordinate descent algorithm for optimizing a non-convex objective function subject to one linear constraint and simple bounds on the variables. Although it is common use to update only two random coordinates simultaneously in each iteration of a coordinate descent algorithm, our...

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Bibliographic Details
Published inJournal of global optimization Vol. 90; no. 4; pp. 843 - 868
Main Authors Ghaffari-Hadigheh, A., Sinjorgo, L., Sotirov, R.
Format Journal Article
LanguageEnglish
Published New York Springer US 01.12.2024
Springer Nature B.V
Subjects
Algorithms
Computer Science
Convergence
Convex analysis
Eigenvalues
Mathematics
Mathematics and Statistics
Methods
Operations Research/Decision Theory
Optimization
Random variables
Real Functions
Variables
Eigenvalue complementarity problem
90C30
Densest
Random coordinate descent algorithm
90C06
90C26
subgraph problem
Convergence analysis
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ISSN0925-5001
1573-2916
1573-2916
DOI10.1007/s10898-024-01429-6

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Summary:We propose a random coordinate descent algorithm for optimizing a non-convex objective function subject to one linear constraint and simple bounds on the variables. Although it is common use to update only two random coordinates simultaneously in each iteration of a coordinate descent algorithm, our algorithm allows updating arbitrary number of coordinates. We provide a proof of convergence of the algorithm. The convergence rate of the algorithm improves when we update more coordinates per iteration. Numerical experiments on large scale instances of different optimization problems show the benefit of updating many coordinates simultaneously.
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ISSN:0925-5001
1573-2916
1573-2916
DOI:10.1007/s10898-024-01429-6