Generating $\alpha $-dense curves in non-convex sets to solve a class of non-smooth constrained global optimization
<p>This paper deals with the dimensionality reduction approach to study multi-dimensional constrained global optimization problems where the objective function is non-differentiable over a general compact set $D$ of $\mathbb{R}^{n}$ and H\"{o}lderian. The fundamental principle is to provi...
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| Format: | Article |
| Language: | English |
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Croatian Operational Research Society
2019-01-01
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| Series: | Croatian Operational Research Review |
| Online Access: | https://hrcak.srce.hr/file/334184 |
| _version_ | 1818258233781911552 |
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| author | Mohamed Rahal Ziadi Abdelkader Ellaia Rachid |
| author_facet | Mohamed Rahal Ziadi Abdelkader Ellaia Rachid |
| author_sort | Mohamed Rahal |
| collection | DOAJ |
| description | <p>This paper deals with the dimensionality reduction approach to study multi-dimensional constrained global optimization problems where the objective function is non-differentiable over a general compact set $D$ of $\mathbb{R}^{n}$ and H\"{o}lderian. The fundamental principle is to provide explicitly a parametric representation $x_{i}=\ell _{i}(t),1\leq i\leq n$ of $\alpha $-dense curve $\ell_{\alpha }$ in the compact $D$, for $t$ in an interval $\mathbb{I}$ of $\mathbb{R}$, which allows to convert the initial problem to a one dimensional H\"{o}lder unconstrained one. Thus, we can solve the problem by using an efficient algorithm available in the case of functions depending on a single variable. A relation between the parameter $\alpha $ of the curve $\ell _{\alpha }$ and the accuracy of attaining the optimal solution is given. Some concrete $\alpha $ dense curves in a non-convex feasible region $D$ are constructed. The numerical results show that the proposed approach is efficient.</p> |
| first_indexed | 2024-12-12T17:56:18Z |
| format | Article |
| id | doaj.art-ccc72f90b34d4de9b1def95f3a07a5f0 |
| institution | Directory Open Access Journal |
| issn | 1848-0225 1848-9931 |
| language | English |
| last_indexed | 2024-12-12T17:56:18Z |
| publishDate | 2019-01-01 |
| publisher | Croatian Operational Research Society |
| record_format | Article |
| series | Croatian Operational Research Review |
| spelling | doaj.art-ccc72f90b34d4de9b1def95f3a07a5f02022-12-22T00:16:43ZengCroatian Operational Research SocietyCroatian Operational Research Review1848-02251848-99312019-01-0110228931410.17535/crorr.2019.0024229888Generating $\alpha $-dense curves in non-convex sets to solve a class of non-smooth constrained global optimizationMohamed Rahal0Ziadi Abdelkader1Ellaia Rachid2Department of Mathematics, Ferhat Abbas Setif 1, University of SetifDepartment of Mathematics, Ferhat Abbas Setif 1, University of SetifLaboratory of Study and Research for Applied Mathematics, Mohammadia School of Engineers<p>This paper deals with the dimensionality reduction approach to study multi-dimensional constrained global optimization problems where the objective function is non-differentiable over a general compact set $D$ of $\mathbb{R}^{n}$ and H\"{o}lderian. The fundamental principle is to provide explicitly a parametric representation $x_{i}=\ell _{i}(t),1\leq i\leq n$ of $\alpha $-dense curve $\ell_{\alpha }$ in the compact $D$, for $t$ in an interval $\mathbb{I}$ of $\mathbb{R}$, which allows to convert the initial problem to a one dimensional H\"{o}lder unconstrained one. Thus, we can solve the problem by using an efficient algorithm available in the case of functions depending on a single variable. A relation between the parameter $\alpha $ of the curve $\ell _{\alpha }$ and the accuracy of attaining the optimal solution is given. Some concrete $\alpha $ dense curves in a non-convex feasible region $D$ are constructed. The numerical results show that the proposed approach is efficient.</p>https://hrcak.srce.hr/file/334184 |
| spellingShingle | Mohamed Rahal Ziadi Abdelkader Ellaia Rachid Generating $\alpha $-dense curves in non-convex sets to solve a class of non-smooth constrained global optimization Croatian Operational Research Review |
| title | Generating $\alpha $-dense curves in non-convex sets to solve a class of non-smooth constrained global optimization |
| title_full | Generating $\alpha $-dense curves in non-convex sets to solve a class of non-smooth constrained global optimization |
| title_fullStr | Generating $\alpha $-dense curves in non-convex sets to solve a class of non-smooth constrained global optimization |
| title_full_unstemmed | Generating $\alpha $-dense curves in non-convex sets to solve a class of non-smooth constrained global optimization |
| title_short | Generating $\alpha $-dense curves in non-convex sets to solve a class of non-smooth constrained global optimization |
| title_sort | generating alpha dense curves in non convex sets to solve a class of non smooth constrained global optimization |
| url | https://hrcak.srce.hr/file/334184 |
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