Convergence of the proximal bundle algorithm for nonsmooth nonconvex optimization problems

被引：0
作者：
N. Hoseini Monjezi
S. Nobakhtian
机构：
[1] Institute for Research in Fundamental Sciences (IPM),School of Mathematics
[2] University of Isfahan,Department of Applied Mathematics and Computer Science, Faculty of Mathematics and Statistics
来源：
Optimization Letters | 2022年 / 16卷
关键词：
Proximal bundle method; Nonsmooth optimization; Nonconvex optimization; Global convergence;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
A proximal bundle algorithm is proposed for solving unconstrained nonsmooth nonconvex optimization problems. At each iteration, using already generated information, the algorithm defines a convex model of the augmented objective function. Then by solving a quadratic subproblem a new candidate iterate is obtained and the algorithm is repeated. The novelty in our approach is that the objective function can be any arbitrary locally Lipschitz function without any additional assumptions. The global convergence, starting from any point, is also studied. At the end, some encouraging numerical results with a MATLAB implementation are reported.
引用
收藏
页码：1495 / 1511
页数：16
相关论文
共 46 条
[11]  
Burke J(2019)A new infeasible proximal bundle algorithm for nonsmooth nonconvex constrained optimization Comput. Optim. Appl. 74 443-480
[12]  
Lewis A(2021)A proximal bundle-based algorithm for nonsmooth constrained multiobjective optimization problems with inexact data Numer. Algor. 141 135-163
[13]  
Overton M(2020)An inexact multiple proximal bundle algorithm for nonsmooth nonconvex multiobjective optimization problems Ann. Oper. Res. 7 533-545
[14]  
Dao MN(2013)Nonsmooth Optimization via Quasi-Newton Methods Math. Program. 68 501-535
[15]  
Dao MN(2013)Conjugate gradient type methods for the nondifferentiable convex minimization Optim. Lett. 10 185-194
[16]  
Gwinner J(2017)A proximal bundle method for nonsmooth DC optimization utilizing nonconvex cutting planes J. Glob. Optim. 18 379-388
[17]  
Noll D(1985)A linearization algorithm for nonsmooth minimization Math. Oper. Res. 18 531-568
[18]  
Ovcharova N(2007)Convergence of the gradient sampling algorithm for nonsmooth nonconvex optimization SIAM J. Optim. 14 1615-1625
[19]  
Dolan ED(2010)Cutting plane oracles to minimize non-smooth non-convex functions Set-Valued Var. Anal. undefined undefined-undefined
[20]  
Moré JJ(2020)Convergence of a stochastic subgradient method with averaging for nonsmooth nonconvex constrained optimization Optim. Lett. undefined undefined-undefined
12345