Bundle trust region algorithm based on linear subproblem

Bundle algorithms are currently considered as the most efficient methods for nonsmooth optimization. In most existing bundle methods (proximal, level, and trust region versions), it is necessary to solve at least one quadratic subproblem at each iteration. In this paper, a new bundle trust region al...

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Bibliographic Details
Published inJournal of global optimization Vol. 92; no. 1; pp. 87 - 109
Main Author Hoseini Monjezi, Najmeh
Format Journal Article
LanguageEnglish
Published New York Springer US 01.05.2025
Springer Nature B.V
Subjects
Algorithms
Applied mathematics
Computer Science
Convex analysis
Linear programming
Lipschitz condition
Mathematics
Mathematics and Statistics
Methods
Norms
Operations Research/Decision Theory
Optimization
Real Functions
Global convergence
Nonconvex optimization
65K05
49J52
Linear programming
Nonsmooth optimization
90C26
90C05
Bundle method
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Summary:Bundle algorithms are currently considered as the most efficient methods for nonsmooth optimization. In most existing bundle methods (proximal, level, and trust region versions), it is necessary to solve at least one quadratic subproblem at each iteration. In this paper, a new bundle trust region algorithm with linear programming subproblems is proposed for solving nonsmooth nonconvex optimization problems. At each iteration, a piecewise linear model is defined, and using the infinity norm and the trust region technique, a linear subproblem is generalized. The algorithm is studied from both theoretical and practical points of view. Under the locally Lipschitz assumption on the objective function, global convergence of it is verified to stationary points. In the end, some encouraging numerical results with a MATLAB implementation are also reported. Computational results show that the developed method is efficient and robust for solving nonsmooth problems.
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ISSN:0925-5001
1573-2916
DOI:10.1007/s10898-025-01485-6