A Modified Level Bundle Method with Inexact Data for Nonsmooth Constrained Optimization

2019 ◽  
Vol 08 (09) ◽  
pp. 1530-1538
Author(s):  
艳妮 李
Keyword(s):  
Constrained Optimization ◽  
Bundle Method ◽  
Inexact Data ◽  
Level Bundle Method

scholarly journals A Cutting Plane and Level Stabilization Bundle Method with Inexact Data for Minimizing Nonsmooth Nonconvex Functions

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Jie Shen ◽  
Dan Li ◽  
Li-Ping Pang
Keyword(s):  
Objective Function ◽  
Cutting Plane ◽  
Bundle Method ◽  
Approximation Model ◽  
Nonconvex Functions ◽  
Proximal Bundle Methods ◽  
New Variant ◽  
Optimal Value ◽  
Inexact Data ◽  
Optimality Gap

Under the condition that the values of the objective function and its subgradient are computed approximately, we introduce a cutting plane and level bundle method for minimizing nonsmooth nonconvex functions by combining cutting plane method with the ideas of proximity control and level constraint. The proposed algorithm is based on the construction of both a lower and an upper polyhedral approximation model to the objective function and calculates new iteration points by solving a subproblem in which the model is employed not only in the objective function but also in the constraints. Compared with other proximal bundle methods, the new variant updates the lower bound of the optimal value, providing an additional useful stopping test based on the optimality gap. Another merit is that our algorithm makes a distinction between affine pieces that exhibit a convex or a concave behavior relative to the current iterate. Convergence to some kind of stationarity point is proved under some looser conditions.

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