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| Paper IPM / M / 18320 |
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| Abstract: | |
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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 aMATLAB
implementation are also reported. Computational results show that the developed method is
efficient and robust for solving nonsmooth problems.
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