scholarly journals Using a Conic Bundle Method to Accelerate Both Phases of a Quadratic Convex Reformulation

2017 ◽  
Vol 29 (2) ◽  
pp. 318-331 ◽  
Author(s):  
Alain Billionnet ◽  
Sourour Elloumi ◽  
Amélie Lambert ◽  
Angelika Wiegele
Keyword(s):  
Bundle Method ◽  
Conic Bundle ◽  
Quadratic Convex Reformulation

scholarly journals Nonsmooth Recursive Identification of Sandwich Systems with Backlash-Like Hysteresis

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
Ruili Dong ◽  
Yonghong Tan ◽  
Hui Chen ◽  
Yangqiu Xie
Keyword(s):  
Estimation Algorithm ◽  
Dynamic Parameter ◽  
Bundle Method ◽  
Recursive Identification ◽  
Identification Algorithm ◽  
Nonsmooth Problem ◽  
Positioning Stage ◽  
Dynamic Parameter Estimation ◽  
Estimation Scheme ◽  
Sandwich System

A recursive gradient identification algorithm based on the bundle method for sandwich systems with backlash-like hysteresis is presented in this paper. In this method, a dynamic parameter estimation scheme based on a subgradient is developed to handle the nonsmooth problem caused by the backlash embedded in the system. The search direction of the algorithm is estimated based on the so-called bundle method. Then, the convergence of the algorithm is discussed. After that, simulation results on a nonsmooth sandwich system are presented to validate the proposed estimation algorithm. Finally, the application of the proposed method to anX-Ymoving positioning stage is illustrated.

A Bundle Method for Solving Variational Inequalities

2004 ◽  
Vol 14 (3) ◽  
pp. 869-893 ◽  
Author(s):  
Geneviève Salmon ◽  
Jean-Jacques Strodiot ◽  
Van Hien Nguyen
Keyword(s):  
Variational Inequalities ◽  
Bundle Method

Design of a flight control architecture using a non-convex bundle method

2012 ◽  
Vol 25 (2) ◽  
pp. 257-290 ◽  
Author(s):  
Marion Gabarrou ◽  
Daniel Alazard ◽  
Dominikus Noll
Keyword(s):  
Flight Control ◽  
Bundle Method ◽  
Control Architecture

scholarly journals Quadratic 0–1 programming: Tightening linear or quadratic convex reformulation by use of relaxations

2008 ◽  
Vol 42 (2) ◽  
pp. 103-121 ◽  
Author(s):  
Alain Billionnet ◽  
Sourour Elloumi ◽  
Marie-Christine Plateau
Keyword(s):  
Quadratic Convex Reformulation

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.

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