Constrained Nonconvex Nonsmooth Optimization via Proximal Bundle Method

2014 ◽  
Vol 163 (3) ◽  
pp. 900-925 ◽  
Author(s):  
Yang Yang ◽  
Liping Pang ◽  
Xuefei Ma ◽  
Jie Shen
Keyword(s):  
Nonsmooth Optimization ◽  
Bundle Method ◽  
Proximal Bundle Method ◽  
Nonconvex Nonsmooth Optimization

A Proximal Bundle Method with Exact Penalty Technique and Bundle Modification Strategy for Nonconvex Nonsmooth Constrained Optimization

2021 ◽  
pp. 2150015
Author(s):  
Xiaoliang Wang ◽  
Liping Pang ◽  
Qi Wu
Keyword(s):  
Operation Research ◽  
Bundle Method ◽  
Exact Penalty ◽  
Constraint Function ◽  
Modified Model ◽  
Proximal Bundle Method ◽  
Unconstrained Problem ◽  
Unconstrained Problems ◽  
Penalty Strategy ◽  
Penalty Technique

The bundle modification strategy for the convex unconstrained problems was proposed by Alexey et al. [[2007] European Journal of Operation Research, 180(1), 38–47.] whose most interesting feature was the reduction of the calls for the quadratic programming solver. In this paper, we extend the bundle modification strategy to a class of nonconvex nonsmooth constraint problems. Concretely, we adopt the convexification technique to the objective function and constraint function, take the penalty strategy to transfer the modified model into an unconstrained optimization and focus on the unconstrained problem with proximal bundle method and the bundle modification strategies. The global convergence of the corresponding algorithm is proved. The primal numerical results show that the proposed algorithms are promising and effective.

scholarly journals Nonconvex nonsmooth optimization via convex–nonconvex majorization–minimization

2016 ◽  
Vol 136 (2) ◽  
pp. 343-381 ◽  
Author(s):  
A. Lanza ◽  
S. Morigi ◽  
I. Selesnick ◽  
F. Sgallari
Keyword(s):  
Nonsmooth Optimization ◽  
Nonconvex Nonsmooth Optimization

scholarly journals An Approximate Proximal Bundle Method to Minimize a Class of Maximum Eigenvalue Functions

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Wei Wang ◽  
Lingling Zhang ◽  
Miao Chen ◽  
Sida Lin
Keyword(s):  
Objective Function ◽  
Optimal Solution ◽  
Cutting Plane ◽  
Bundle Method ◽  
Maximum Eigenvalue ◽  
Plane Model ◽  
Essential Idea ◽  
Proximal Bundle Method ◽  
The Difference ◽  
And Function

We present an approximate nonsmooth algorithm to solve a minimization problem, in which the objective function is the sum of a maximum eigenvalue function of matrices and a convex function. The essential idea to solve the optimization problem in this paper is similar to the thought of proximal bundle method, but the difference is that we choose approximate subgradient and function value to construct approximate cutting-plane model to solve the above mentioned problem. An important advantage of the approximate cutting-plane model for objective function is that it is more stable than cutting-plane model. In addition, the approximate proximal bundle method algorithm can be given. Furthermore, the sequences generated by the algorithm converge to the optimal solution of the original problem.

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