An augmented subgradient method for minimizing nonsmooth DC functions

A method, called an augmented subgradient method, is developed to solve unconstrained nonsmooth difference of convex (DC) optimization problems. At each iteration of this method search directions are found by using several subgradients of the first DC component and one subgradient of the second DC c...

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Published in:Computational optimization and applications 2021-11, Vol.80 (2), p.411-438
Main Authors: Bagirov, A. M., Hoseini Monjezi, N., Taheri, S.
Format: Article
Language:English
Subjects:
Convex and Discrete Geometry
Critical point
Iterative methods
Management Science
Mathematics
Mathematics and Statistics
Operations Research
Operations Research/Decision Theory
Optimization
Solvers
Statistics
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description A method, called an augmented subgradient method, is developed to solve unconstrained nonsmooth difference of convex (DC) optimization problems. At each iteration of this method search directions are found by using several subgradients of the first DC component and one subgradient of the second DC component of the objective function. The developed method applies an Armijo-type line search procedure to find the next iteration point. It is proved that the sequence of points generated by the method converges to a critical point of the unconstrained DC optimization problem. The performance of the method is demonstrated using academic test problems with nonsmooth DC objective functions and its performance is compared with that of two general nonsmooth optimization solvers and five solvers specifically designed for unconstrained DC optimization. Computational results show that the developed method is efficient and robust for solving nonsmooth DC optimization problems.
doi_str_mv 10.1007/s10589-021-00304-4
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subjects Convex and Discrete Geometry
Critical point
Iterative methods
Management Science
Mathematics
Mathematics and Statistics
Operations Research
Operations Research/Decision Theory
Optimization
Solvers
Statistics
title An augmented subgradient method for minimizing nonsmooth DC functions
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