An affine scaling interior trust region method via optimal path for solving monotone variational inequality problem with linear constraints

2008 ◽  
Vol 29 (3) ◽  
pp. 273-290
Author(s):  
Yunjuan Wang ◽  
Detong Zhu
Keyword(s):  
Variational Inequality ◽  
Variational Inequality Problem ◽  
Optimal Path ◽  
Trust Region Method ◽  
Trust Region ◽  
Linear Constraints ◽  
Affine Scaling ◽  
Inequality Problem ◽  
Region Method ◽  
Monotone Variational Inequality

A Regularized Affine-Scaling Trust-Region Method for Parametric Imaging of Dynamic PET Data

2021 ◽  
Vol 14 (1) ◽  
pp. 418-439
Author(s):  
S. Crisci ◽  
M. Piana ◽  
V. Ruggiero ◽  
M. Scussolini
Keyword(s):  
Trust Region Method ◽  
Trust Region ◽  
Affine Scaling ◽  
Parametric Imaging ◽  
Dynamic Pet ◽  
Region Method

scholarly journals On the $O(1/k)$ Convergence Rate of He's Alternating Directions Method for a Kind of Structured Variational Inequality Problem

2015 ◽  
Vol 7 (2) ◽  
pp. 69
Author(s):  
Haiwen Xu
Keyword(s):  
Variational Inequality ◽  
Convergence Rate ◽  
Variational Inequality Problem ◽  
Variational Inequality Problems ◽  
System Of Nonlinear Equations ◽  
Inequality Problem ◽  
Quadratic Minimization ◽  
Projection And Contraction Methods ◽  
Monotone Variational Inequality ◽  
Alternating Directions Method

The  alternating directions method for a kind of structured variational inequality problem (He, 2001) is an attractive method for structured monotone variational inequality problems. In each iteration, the subproblemsare  convex quadratic minimization problem with simple constraintsand a well-conditioned system of nonlinear equations that can be efficiently solvedusing classical methods. Researchers have recently described the convergence rateof projection and contraction methods for variational inequality problems andthe original ADM and its linearized variant. Motivated and inspired by researchinto the convergence rate of these methods, we provide a simple proof to show the $O(1/k)$ convergencerate of  alternating directions methods for structured monotone variational inequality problems (He, 2001).

Nonmonotone conic trust region method with line search technique for bound constrained optimization

2019 ◽  
Vol 53 (3) ◽  
pp. 787-805
Author(s):  
Lijuan Zhao
Keyword(s):  
Constrained Optimization ◽  
Line Search ◽  
Optimization Problems ◽  
Trust Region Method ◽  
Trust Region ◽  
Affine Scaling ◽  
Search Technique ◽  
Region Method ◽  
Bound Constrained Optimization ◽  
Line Search Technique

In this paper, we propose a nonmonotone trust region method for bound constrained optimization problems, where the bounds are dealt with by affine scaling technique. Differing from the traditional trust region methods, the subproblem in our algorithm is based on a conic model. Moreover, when the trial point isn’t acceptable by the usual trust region criterion, a line search technique is used to find an acceptable point. This procedure avoids resolving the trust region subproblem, which may reduce the total computational cost. The global convergence and Q-superlinear convergence of the algorithm are established under some mild conditions. Numerical results on a series of standard test problems are reported to show the effectiveness of the new method.

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