Convergence of the proximal bundle algorithm for nonsmooth nonconvex optimization problems

2021 ◽  
Author(s):  
N. Hoseini Monjezi ◽  
S. Nobakhtian
Keyword(s):  
Nonconvex Optimization ◽  
Optimization Problems ◽  
Nonconvex Optimization Problems ◽  
Nonsmooth Nonconvex Optimization ◽  
Bundle Algorithm

scholarly journals Random perturbation of the projected variable metric method for nonsmooth nonconvex optimization problems with linear constraints

2011 ◽  
Vol 21 (2) ◽  
pp. 317-329 ◽  
Author(s):  
Abdelkrim El Mouatasim ◽  
Rachid Ellaia ◽  
Eduardo de Cursi
Keyword(s):  
Nonconvex Optimization ◽  
Optimization Problems ◽  
Random Perturbation ◽  
Linear Constraints ◽  
Nonconvex Optimization Problems ◽  
Variable Metric ◽  
Lipschitz Continuous ◽  
Nonsmooth Nonconvex Optimization ◽  
Variable Metric Method ◽  
Set Of Points

Random perturbation of the projected variable metric method for nonsmooth nonconvex optimization problems with linear constraintsWe present a random perturbation of the projected variable metric method for solving linearly constrained nonsmooth (i.e., nondifferentiable) nonconvex optimization problems, and we establish the convergence to a global minimum for a locally Lipschitz continuous objective function which may be nondifferentiable on a countable set of points. Numerical results show the effectiveness of the proposed approach.

scholarly journals A Decomposition Method with Redistributed Subroutine for Constrained Nonconvex Optimization

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Yuan Lu ◽  
Wei Wang ◽  
Li-Ping Pang ◽  
Dan Li
Keyword(s):  
Programming Problem ◽  
Nonconvex Optimization ◽  
Decomposition Method ◽  
Optimization Problems ◽  
Inequality Constraints ◽  
Nonconvex Optimization Problems ◽  
Cone Programming ◽  
Nonsmooth Nonconvex Optimization ◽  
Second Order Cone ◽  
Convergent Method

A class of constrained nonsmooth nonconvex optimization problems, that is, piecewiseC2objectives with smooth inequality constraints are discussed in this paper. Based on the𝒱𝒰-theory, a superlinear convergent𝒱𝒰-algorithm, which uses a nonconvex redistributed proximal bundle subroutine, is designed to solve these optimization problems. An illustrative example is given to show how this convergent method works on a Second-Order Cone programming problem.

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