Stochastic Smoothing Methods for Nonsmooth Global Optimization
Abstract. The paper presents the results of testing the stochastic smoothing method for global optimization of a multiextremal function in a convex feasible subset of Euclidean space. Preliminarily, the objective function is extended outside the admissible region so that its global minimum does not...
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| Format: | Article |
| Language: | English |
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V.M. Glushkov Institute of Cybernetics
2020-03-01
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| Series: | Кібернетика та комп'ютерні технології |
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| Online Access: | http://cctech.org.ua/13-vertikalnoe-menyu-en/89-abstract-20-1-1-arte |
| _version_ | 1811256408357732352 |
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| author | V.I. Norkin |
| author_facet | V.I. Norkin |
| author_sort | V.I. Norkin |
| collection | DOAJ |
| description | Abstract. The paper presents the results of testing the stochastic smoothing method for global optimization of a multiextremal function in a convex feasible subset of Euclidean space. Preliminarily, the objective function is extended outside the admissible region so that its global minimum does not change, and it becomes coercive. The smoothing of a function at any point is carried out by averaging the values of the function over some neighborhood of this point. The size of the neighborhood is a smoothing parameter. Smoothing eliminates small local extrema of the original function. With a sufficiently large value of the smoothing parameter, the averaged function can have only one minimum. The smoothing method consists in replacing the original function with a sequence of smoothed approximations with vanishing to zero smoothing parameter and optimization of the latter functions by contemporary stochastic optimization methods. Passing from the minimum of one smoothed function to a close minimum of the next smoothed function, we can gradually come to the region of the global minimum of the original function. The smoothing method is also applicable for the optimization of nonsmooth nonconvex functions. It is shown that the smoothing method steadily solves test global optimization problems of small dimensions from the literature. |
| first_indexed | 2024-04-12T17:40:39Z |
| format | Article |
| id | doaj.art-b1e4fe06d2e34d71b625edc4dda945b9 |
| institution | Directory Open Access Journal |
| issn | 2707-4501 2707-451X |
| language | English |
| last_indexed | 2024-04-12T17:40:39Z |
| publishDate | 2020-03-01 |
| publisher | V.M. Glushkov Institute of Cybernetics |
| record_format | Article |
| series | Кібернетика та комп'ютерні технології |
| spelling | doaj.art-b1e4fe06d2e34d71b625edc4dda945b92022-12-22T03:22:49ZengV.M. Glushkov Institute of CyberneticsКібернетика та комп'ютерні технології2707-45012707-451X2020-03-01151410.34229/2707-451X.20.1.110-34229-2707-451X-20-1-1Stochastic Smoothing Methods for Nonsmooth Global OptimizationV.I. Norkin0https://orcid.org/0000-0003-3255-0405V.M. Glushkov Institute of Cybernetics, Kyiv, UkraineAbstract. The paper presents the results of testing the stochastic smoothing method for global optimization of a multiextremal function in a convex feasible subset of Euclidean space. Preliminarily, the objective function is extended outside the admissible region so that its global minimum does not change, and it becomes coercive. The smoothing of a function at any point is carried out by averaging the values of the function over some neighborhood of this point. The size of the neighborhood is a smoothing parameter. Smoothing eliminates small local extrema of the original function. With a sufficiently large value of the smoothing parameter, the averaged function can have only one minimum. The smoothing method consists in replacing the original function with a sequence of smoothed approximations with vanishing to zero smoothing parameter and optimization of the latter functions by contemporary stochastic optimization methods. Passing from the minimum of one smoothed function to a close minimum of the next smoothed function, we can gradually come to the region of the global minimum of the original function. The smoothing method is also applicable for the optimization of nonsmooth nonconvex functions. It is shown that the smoothing method steadily solves test global optimization problems of small dimensions from the literature.http://cctech.org.ua/13-vertikalnoe-menyu-en/89-abstract-20-1-1-arteglobal optimizationsteklov smoothingaveraged functionsstochastic optimizationnonsmooth nonconvex optimization |
| spellingShingle | V.I. Norkin Stochastic Smoothing Methods for Nonsmooth Global Optimization Кібернетика та комп'ютерні технології global optimization steklov smoothing averaged functions stochastic optimization nonsmooth nonconvex optimization |
| title | Stochastic Smoothing Methods for Nonsmooth Global Optimization |
| title_full | Stochastic Smoothing Methods for Nonsmooth Global Optimization |
| title_fullStr | Stochastic Smoothing Methods for Nonsmooth Global Optimization |
| title_full_unstemmed | Stochastic Smoothing Methods for Nonsmooth Global Optimization |
| title_short | Stochastic Smoothing Methods for Nonsmooth Global Optimization |
| title_sort | stochastic smoothing methods for nonsmooth global optimization |
| topic | global optimization steklov smoothing averaged functions stochastic optimization nonsmooth nonconvex optimization |
| url | http://cctech.org.ua/13-vertikalnoe-menyu-en/89-abstract-20-1-1-arte |
| work_keys_str_mv | AT vinorkin stochasticsmoothingmethodsfornonsmoothglobaloptimization |