An active set trust region method for general bound constrained optimization

2011 ◽  
Vol 41 (4) ◽  
pp. 377-391
Author(s):  
Xiao WANG
Keyword(s):  
Constrained Optimization ◽  
Trust Region Method ◽  
Trust Region ◽  
Active Set ◽  
Region Method ◽  
Bound Constrained Optimization ◽  
General Bound

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.

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.

Numerical experience with a recursive trust-region method for multilevel nonlinear bound-constrained optimization

2010 ◽  
Vol 25 (3) ◽  
pp. 359-386 ◽  
Author(s):  
Serge Gratton ◽  
Mélodie Mouffe ◽  
Annick Sartenaer ◽  
Philippe L. Toint ◽  
Dimitri Tomanos
Keyword(s):  
Constrained Optimization ◽  
Trust Region Method ◽  
Trust Region ◽  
Numerical Experience ◽  
Region Method ◽  
Bound Constrained Optimization
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