scholarly journals A New Filter Nonmonotone Adaptive Trust Region Method for Unconstrained Optimization

Symmetry ◽  
2020 ◽  
Vol 12 (2) ◽  
pp. 208 ◽  
Author(s):  
Xinyi Wang ◽  
Xianfeng Ding ◽  
Quan Qu
Keyword(s):  
Unconstrained Optimization ◽  
Symmetric Matrix ◽  
Hessian Matrix ◽  
Trust Region Method ◽  
Trust Region ◽  
Adaptive Strategy ◽  
Step Length ◽  
Computational Costs ◽  
Definite Symmetric Matrix ◽  
Approximate Hessian

In this paper, a new filter nonmonotone adaptive trust region with fixed step length for unconstrained optimization is proposed. The trust region radius adopts a new adaptive strategy to overcome additional computational costs at each iteration. A new nonmonotone trust region ratio is introduced. When a trial step is not successful, a multidimensional filter is employed to increase the possibility of the trial step being accepted. If the trial step is still not accepted by the filter set, it is possible to find a new iteration point along the trial step and the step length is computed by a fixed formula. The positive definite symmetric matrix of the approximate Hessian matrix is updated using the MBFGS method. The global convergence and superlinear convergence of the proposed algorithm is proven by some classical assumptions. The efficiency of the algorithm is tested by numerical results.

scholarly journals A nonmonotone modified BFGS algorithm for nonconvex unconstrained optimization problems

Filomat ◽  
2016 ◽  
Vol 30 (5) ◽  
pp. 1283-1296
Author(s):  
Keyvan Amini ◽  
Somayeh Bahrami ◽  
Shadi Amiri
Keyword(s):  
Unconstrained Optimization ◽  
Line Search ◽  
Optimization Problems ◽  
Hessian Matrix ◽  
Convergence Properties ◽  
Convexity Assumption ◽  
Unconstrained Optimization Problems ◽  
Secant Condition ◽  
Approximate Hessian ◽  
Modified Secant Condition

In this paper, a modified BFGS algorithm is proposed to solve unconstrained optimization problems. First, based on a modified secant condition, an update formula is recommended to approximate Hessian matrix. Then thanks to the remarkable nonmonotone line search properties, an appropriate nonmonotone idea is employed. Under some mild conditions, the global convergence properties of the algorithm are established without convexity assumption on the objective function. Preliminary numerical experiments are also reported which indicate the promising behavior of the new algorithm.

A randomized nonmonotone adaptive trust region method based on the simulated annealing strategy for unconstrained optimization

2019 ◽  
Vol 12 (3) ◽  
pp. 389-399
Author(s):  
Saman Babaie-Kafaki ◽  
Saeed Rezaee
Keyword(s):  
Simulated Annealing ◽  
Unconstrained Optimization ◽  
Optimization Problems ◽  
Trust Region Method ◽  
Trust Region ◽  
Test Problems ◽  
Content Type ◽  
Unconstrained Optimization Problems ◽  
Randomization Scheme ◽  
Enhance Efficiency

PurposeThe purpose of this paper is to employ stochastic techniques to increase efficiency of the classical algorithms for solving nonlinear optimization problems.Design/methodology/approachThe well-known simulated annealing strategy is employed to search successive neighborhoods of the classical trust region (TR) algorithm.FindingsAn adaptive formula for computing the TR radius is suggested based on an eigenvalue analysis conducted on the memoryless Broyden-Fletcher-Goldfarb-Shanno updating formula. Also, a (heuristic) randomized adaptive TR algorithm is developed for solving unconstrained optimization problems. Results of computational experiments on a set of CUTEr test problems show that the proposed randomization scheme can enhance efficiency of the TR methods.Practical implicationsThe algorithm can be effectively used for solving the optimization problems which appear in engineering, economics, management, industry and other areas.Originality/valueThe proposed randomization scheme improves computational costs of the classical TR algorithm. Especially, the suggested algorithm avoids resolving the TR subproblems for many times.

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.

scholarly journals AN IMPROVED ADAPTIVE TRUST-REGION METHOD FOR UNCONSTRAINED OPTIMIZATION

2014 ◽  
Vol 19 (4) ◽  
pp. 469-490 ◽  
Author(s):  
Hamid Esmaeili ◽  
Morteza Kimiaei
Keyword(s):  
Unconstrained Optimization ◽  
Large Scale ◽  
Optimization Problems ◽  
Trust Region Method ◽  
Trust Region ◽  
Standard Test ◽  
Test Problems ◽  
Unconstrained Optimization Problems ◽  
Large Scale Problems ◽  
Adaptive Radius

In this study, we propose a trust-region-based procedure to solve unconstrained optimization problems that take advantage of the nonmonotone technique to introduce an efficient adaptive radius strategy. In our approach, the adaptive technique leads to decreasing the total number of iterations, while utilizing the structure of nonmonotone formula helps us to handle large-scale problems. The new algorithm preserves the global convergence and has quadratic convergence under suitable conditions. Preliminary numerical experiments on standard test problems indicate the efficiency and robustness of the proposed approach for solving unconstrained optimization problems.

Sign in / Sign up

Export Citation Format

Share Document