A Trust Region Algorithm for Equality Constrained Minimization: Convergence Properties and Implementation

1985 ◽  
Vol 22 (3) ◽  
pp. 575-591 ◽  
Author(s):  
Avi Vardi
Keyword(s):  
Trust Region ◽  
Constrained Minimization ◽  
Convergence Properties ◽  
Trust Region Algorithm

scholarly journals A Novel Self-Adaptive Trust Region Algorithm for Unconstrained Optimization

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Yunlong Lu ◽  
Wenyu Li ◽  
Mingyuan Cao ◽  
Yueting Yang
Keyword(s):  
Objective Function ◽  
Unconstrained Optimization ◽  
Optimization Problems ◽  
Trust Region Method ◽  
Trust Region ◽  
Convergence Properties ◽  
Trust Region Algorithm ◽  
Unconstrained Optimization Problems ◽  
Piecewise Function ◽  
Self Adaptive

A new self-adaptive rule of trust region radius is introduced, which is given by a piecewise function on the ratio between the actual and predicted reductions of the objective function. A self-adaptive trust region method for unconstrained optimization problems is presented. The convergence properties of the method are established under reasonable assumptions. Preliminary numerical results show that the new method is significant and robust for solving unconstrained optimization problems.

A new trust region algorithm for bound constrained minimization

1994 ◽  
Vol 30 (3) ◽  
pp. 235-266 ◽  
Author(s):  
A. Friedlander ◽  
J. M. Mart�nez ◽  
S. A. Santos
Keyword(s):  
Trust Region ◽  
Constrained Minimization ◽  
Trust Region Algorithm ◽  
Bound Constrained Minimization

scholarly journals A new trust region method for nonsmooth equations

2003 ◽  
Vol 44 (4) ◽  
pp. 595-607 ◽  
Author(s):  
Y. F. Yang
Keyword(s):  
Global Convergence ◽  
Smooth Function ◽  
Trust Region Method ◽  
Trust Region ◽  
Nonsmooth Equations ◽  
Trust Region Methods ◽  
Convergence Properties ◽  
Trust Region Algorithm ◽  
Consistency Property ◽  
Quadratical Convergence

AbstractWe propose a new trust region algorithm for solving the system of nonsmooth equations F(x) = 0 by using a smooth function satisfying the Jacobian consistency property to approximate the nonsmooth function F(x). Compared with existing trust region methods for systems of nonsmooth equations, the proposed algorithm possesses some nice convergence properties. Global convergence is established and, in particular, locally superlinear or quadratical convergence is obtained if F is semismooth or strongly semismooth at the solution.

scholarly journals Modeling and Fault Diagnosis of Interturn Short Circuit for Five-Phase Permanent Magnet Synchronous Motor

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Jian-wei Yang ◽  
Man-feng Dou ◽  
Zhi-yong Dai
Keyword(s):  
Parameter Estimation ◽  
Fault Diagnosis ◽  
Permanent Magnet ◽  
Fault Tolerant ◽  
Short Circuit ◽  
Estimation Method ◽  
Trust Region ◽  
Fault Tolerant Control ◽  
Trust Region Algorithm ◽  
Parameter Estimation Method

Taking advantage of the high reliability, multiphase permanent magnet synchronous motors (PMSMs), such as five-phase PMSM and six-phase PMSM, are widely used in fault-tolerant control applications. And one of the important fault-tolerant control problems is fault diagnosis. In most existing literatures, the fault diagnosis problem focuses on the three-phase PMSM. In this paper, compared to the most existing fault diagnosis approaches, a fault diagnosis method for Interturn short circuit (ITSC) fault of five-phase PMSM based on the trust region algorithm is presented. This paper has two contributions. (1) Analyzing the physical parameters of the motor, such as resistances and inductances, a novel mathematic model for ITSC fault of five-phase PMSM is established. (2) Introducing an object function related to the Interturn short circuit ratio, the fault parameters identification problem is reformulated as the extreme seeking problem. A trust region algorithm based parameter estimation method is proposed for tracking the actual Interturn short circuit ratio. The simulation and experimental results have validated the effectiveness of the proposed parameter estimation method.

scholarly journals A Nonmonotone Weighting Self-Adaptive Trust Region Algorithm for Unconstrained Nonconvex Optimization

2015 ◽  
Vol 2015 ◽  
pp. 1-8
Author(s):  
Yunlong Lu ◽  
Weiwei Yang ◽  
Wenyu Li ◽  
Xiaowei Jiang ◽  
Yueting Yang
Keyword(s):  
Nonconvex Optimization ◽  
Line Search ◽  
Optimization Problems ◽  
Trust Region Method ◽  
Trust Region ◽  
Search Technique ◽  
Trust Region Algorithm ◽  
Unconstrained Optimization Problems ◽  
Line Search Technique ◽  
Self Adaptive

A new trust region method is presented, which combines nonmonotone line search technique, a self-adaptive update rule for the trust region radius, and the weighting technique for the ratio between the actual reduction and the predicted reduction. Under reasonable assumptions, the global convergence of the method is established for unconstrained nonconvex optimization. Numerical results show that the new method is efficient and robust for solving unconstrained optimization problems.

Sign in / Sign up

Export Citation Format

Share Document