A trust region algorithm with a worst-case iteration complexity of $$\mathcal{O}(\epsilon ^{-3/2})$$ O ( ϵ - 3 / 2 ) for nonconvex optimization

2016 ◽  
Vol 162 (1-2) ◽  
pp. 1-32 ◽  
Author(s):  
Frank E. Curtis ◽  
Daniel P. Robinson ◽  
Mohammadreza Samadi
Keyword(s):  
Nonconvex Optimization ◽  
Trust Region ◽  
Iteration Complexity ◽  
Worst Case ◽  
Trust Region Algorithm

scholarly journals An inexact regularized Newton framework with a worst-case iteration complexity of $ {\mathscr O}(\varepsilon^{-3/2}) $ for nonconvex optimization

2018 ◽  
Vol 39 (3) ◽  
pp. 1296-1327 ◽  
Author(s):  
Frank E Curtis ◽  
Daniel P Robinson ◽  
Mohammadreza Samadi
Keyword(s):  
Nonconvex Optimization ◽  
Optimization Problems ◽  
Trust Region ◽  
Newton Methods ◽  
Positive Real ◽  
Worst Case ◽  
Nonconvex Optimization Problems ◽  
Trust Region Algorithm ◽  
Wide Range ◽  
Regularized Newton Methods

Abstract An algorithm for solving smooth nonconvex optimization problems is proposed that, in the worst-case, takes ${\mathscr O}(\varepsilon ^{-3/2})$ iterations to drive the norm of the gradient of the objective function below a prescribed positive real number $\varepsilon $ and can take ${\mathscr O}(\varepsilon ^{-3})$ iterations to drive the leftmost eigenvalue of the Hessian of the objective above $-\varepsilon $. The proposed algorithm is a general framework that covers a wide range of techniques including quadratically and cubically regularized Newton methods, such as the Adaptive Regularization using Cubics (arc) method and the recently proposed Trust-Region Algorithm with Contractions and Expansions (trace). The generality of our method is achieved through the introduction of generic conditions that each trial step is required to satisfy, which in particular allows for inexact regularized Newton steps to be used. These conditions center around a new subproblem that can be approximately solved to obtain trial steps that satisfy the conditions. A new instance of the framework, distinct from arc and trace, is described that may be viewed as a hybrid between quadratically and cubically regularized Newton methods. Numerical results demonstrate that our hybrid algorithm outperforms a cubically regularized Newton 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.

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.

A novel hybrid trust region algorithm based on nonmonotone and LOOCV techniques

2018 ◽  
Vol 72 (2) ◽  
pp. 499-524
Author(s):  
M. Ahmadvand ◽  
M. Esmaeilbeigi ◽  
A. Kamandi ◽  
F. M. Yaghoobi
Keyword(s):  
Trust Region ◽  
Trust Region Algorithm

scholarly journals A nonmonotone adaptive trust-region algorithm for symmetric nonlinear equations

2010 ◽  
Vol 02 (04) ◽  
pp. 373-378
Author(s):  
Gong-Lin Yuan ◽  
Cui-Ling Chen ◽  
Zeng-Xin Wei
Keyword(s):  
Nonlinear Equations ◽  
Trust Region ◽  
Trust Region Algorithm
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