An active-set projected trust region algorithm for box constrained optimization problems

2014 ◽  
Vol 28 (5) ◽  
pp. 1128-1147 ◽  
Author(s):  
Gonglin Yuan ◽  
Zengxin Wei ◽  
Maojun Zhang
Keyword(s):  
Constrained Optimization ◽  
Optimization Problems ◽  
Trust Region ◽  
Active Set ◽  
Constrained Optimization Problems ◽  
Trust Region Algorithm

scholarly journals An Active Set Trust-Region Method for Bound-Constrained Optimization

2021 ◽  
Author(s):  
Morteza Kimiaei
Keyword(s):  
Constrained Optimization ◽  
Optimization Problems ◽  
Trust Region Method ◽  
Trust Region ◽  
Positive Definiteness ◽  
Active Set ◽  
Sufficient Descent Condition ◽  
Critical Measure ◽  
Complexity Result ◽  
Bound Constrained Optimization

AbstractThis paper discusses an active set trust-region algorithm for bound-constrained optimization problems. A sufficient descent condition is used as a computational measure to identify whether the function value is reduced or not. To get our complexity result, a critical measure is used which is computationally better than the other known critical measures. Under the positive definiteness of approximated Hessian matrices restricted to the subspace of non-active variables, it will be shown that unlimited zigzagging cannot occur. It is shown that our algorithm is competitive in comparison with the state-of-the-art solvers for solving an ill-conditioned bound-constrained least-squares problem.

scholarly journals A Nonmonotone Trust Region Algorithm Based on the Average of the Successive Penalty Function Values for Nonlinear Optimization

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Zhensheng Yu ◽  
Jinhong Yu
Keyword(s):  
Global Convergence ◽  
Penalty Function ◽  
Optimization Problems ◽  
Trust Region ◽  
Trust Region Methods ◽  
Constrained Optimization Problems ◽  
Trust Region Algorithm ◽  
Numerical Tests ◽  
Equality Constrained Optimization ◽  
Nonlinear Equality

We present a nonmonotone trust region algorithm for nonlinear equality constrained optimization problems. In our algorithm, we use the average of the successive penalty function values to rectify the ratio of predicted reduction and the actual reduction. Compared with the existing nonmonotone trust region methods, our method is independent of the nonmonotone parameter. We establish the global convergence of the proposed algorithm and give the numerical tests to show the efficiency of the algorithm.

scholarly journals A Derivative-Free Trust Region Algorithm with Nonmonotone Filter Technique for Bound Constrained Optimization

2018 ◽  
Vol 2018 ◽  
pp. 1-13
Author(s):  
Jing Gao ◽  
Jian Cao ◽  
Yueting Yang
Keyword(s):  
Constrained Optimization ◽  
Optimization Problems ◽  
Trust Region ◽  
Computational Time ◽  
Test Problems ◽  
Trust Region Algorithm ◽  
Filter Technique ◽  
Derivative Free ◽  
Bound Constrained Optimization ◽  
Parameter Values

We propose a derivative-free trust region algorithm with a nonmonotone filter technique for bound constrained optimization. The derivative-free strategy is applied for special minimization functions in which derivatives are not all available. A nonmonotone filter technique ensures not only the trust region feature but also the global convergence under reasonable assumptions. Numerical experiments demonstrate that the new algorithm is effective for bound constrained optimization. Locally, optimal parameters with respect to overall computational time on a set of test problems are identified. The performance of the best choice of parameter values obtained by the algorithm we presented which differs from traditionally used values indicates that the algorithm proposed in this paper has a certain advantage for the nondifferentiable optimization problems.

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