Bundle trust region algorithm based on linear subproblem

Najmeh Hoseini Monjezi ()
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Najmeh Hoseini Monjezi: University of Isfahan

Journal of Global Optimization, 2025, vol. 92, issue 1, No 4, 87-109

Abstract: Abstract 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.

Keywords: Bundle method; Linear programming; Nonsmooth optimization; Nonconvex optimization; Global convergence; 90C26; 65K05; 49J52; 90C05 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10898-025-01485-6

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