Reducing the number of function evaluations in derivative-free algorithm for bound constrained optimization

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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A Modified Derivative-Free Algorithm for Bound Constrained Optimization

2006 International Conference on Machine Learning and Cybernetics ◽

10.1109/icmlc.2006.258666 ◽

2006 ◽

Author(s):

Yan Li ◽

Qing-hua Zhou

Keyword(s):

Constrained Optimization ◽

Derivative Free ◽

Bound Constrained Optimization

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Searching for Multiple Minima of Bound Constrained Optimization Problems using Derivative Free Optimization Techniques

Proceedings of the Eleventh International Conference on Computational Structures Technology ◽

10.4203/ccp.99.63 ◽

2012 ◽

Cited By ~ 1

Author(s):

U.M. García Palomares

Keyword(s):

Constrained Optimization ◽

Optimization Problems ◽

Optimization Techniques ◽

Constrained Optimization Problems ◽

Derivative Free Optimization ◽

Derivative Free ◽

Bound Constrained Optimization ◽

Multiple Minima

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An active-set trust-region method for derivative-free nonlinear bound-constrained optimization

Optimization Methods and Software ◽

10.1080/10556788.2010.549231 ◽

2011 ◽

Vol 26 (4-5) ◽

pp. 873-894 ◽

Cited By ~ 22

Author(s):

Serge Gratton ◽

Philippe L. Toint ◽

Anke Tröltzsch

Keyword(s):

Constrained Optimization ◽

Trust Region Method ◽

Trust Region ◽

Active Set ◽

Region Method ◽

Derivative Free ◽

Bound Constrained Optimization

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

Bulletin of the Iranian Mathematical Society ◽

10.1007/s41980-021-00610-x ◽

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.

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