Test Problems for Lipschitz Univariate Global Optimization with Multiextremal Constraints

Famularo, Domenico; Pugliese, Paolo; Sergeyev, Yaroslav D.

doi:10.1007/0-306-47648-7_6

Cited by 14 publications

(30 citation statements)

References 11 publications

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“…which is some particular case of the method (10). Hence, the superlinear convergence is achieved, when…”

Section: Application In Optimization and Numerical Resultsmentioning

confidence: 96%

A perturbed version of an inexact generalized Newton method for solving nonsmooth equations

Śmietański

2012

Numer Algor

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In this paper, we present the combination of the inexact Newton method and the generalized Newton method for solving nonsmooth equations F(x) = 0, characterizing the local convergence in terms of the perturbations and residuals. We assume that both iteration matrices taken from the B-differential and vectors F(x (k) ) are perturbed at each step. Some results are motivated by the approach of Cȃtinaş regarding to smooth equations. We study the conditions, which determine admissible magnitude of perturbations to preserve the convergence of method. Finally, the utility of these results is considered based on some variant of the perturbed inexact generalized Newton method for solving some general optimization problems.

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“…which is some particular case of the method (10). Hence, the superlinear convergence is achieved, when…”

Section: Application In Optimization and Numerical Resultsmentioning

confidence: 96%

A perturbed version of an inexact generalized Newton method for solving nonsmooth equations

Śmietański

2012

Numer Algor

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“…To illustrate, we apply the above methodology to test problems 5 and 6 adapted from [10] (see Appendix 1 for detailed descriptions of these problems). Figure 8a and c shows the lower bounds on probabilities of improvement corresponding to a = 0 and 1, and Figure 8b and d shows the individual performance of parameterized IHR employing each value of a.…”

Section: Corollary 36 For Lipschitz Continuous Optimization Problemsmentioning

confidence: 99%

Adaptive parameterized improving hit-and-run for global optimization

Wang

Ghate

Zabinsky

2009

Optimization Methods and Software

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We build on improving hit-and-run's (IHR) prior success as a Monte Carlo random search algorithm for global optimization by generalizing the algorithm's sampling distribution. Specifically, in place of the uniform step-size distribution in IHR, we employ a family of parameterized step-size distributions to sample candidate points. The IHR step-size distribution is a special instance within this family. This parameterization is motivated by recent results on efficient decentralized search in the so-called Small World problems. To improve the performance of the algorithm, we adaptively tune the parameter based on the success rate of obtaining improving points. We present analytical and numerical results on simple spherical programmes to illustrate the key ideas of the relationship between the parametrization and algorithm performance. These results are then extended to global optimization problems with Lipschitz continuous objective functions. Our preliminary numerical results demonstrate the potential benefit of considering parameterized versions of IHR.

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“…Further, due to lack of space, we would like to direct the readers to the reference [15] for the details of the the ten test problems (P1 to P10) used in this work to test the performance of our proposed constrained global optimization algorithm.…”

Section: Appendixmentioning

confidence: 99%

Constrained global optimization of non-polynomial problems using the Taylor-Bernstein form

Patil

Nataraj

2015

2015 International Conference on Industrial Instrumentation and Control (ICIC)

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In this paper, we propose a new constrained global optimization algorithm to solve non-polynomial problems. The proposed algorithm is of branch-and-bound type and use the Taylor-Bernstein form as a higher-order inclusion function for the global optimization. Several new ingredients are incorporated in the proposed algorithm to improve its efficiency, such as a improved range estimating technique along with a new simple method to generate the Taylor model of a give function. Further, different numerical experiments are conducted using the proposed algorithm on a set of 10 challenging test problems. The results of the numerical experiments are compared with the MATLAB fmincon solver and are found to be encouraging in terms of the chosen performance metrics.

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Test Problems for Lipschitz Univariate Global Optimization with Multiextremal Constraints

Cited by 14 publications

References 11 publications

A perturbed version of an inexact generalized Newton method for solving nonsmooth equations

A perturbed version of an inexact generalized Newton method for solving nonsmooth equations

Adaptive parameterized improving hit-and-run for global optimization

Constrained global optimization of non-polynomial problems using the Taylor-Bernstein form

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