# Croatian Operational Research Review,Vol. 10 No. 2, 2019.

Izvorni znanstveni članak
https://doi.org/10.17535/crorr.2019.0024

Generating $\alpha$-dense curves in non-convex sets to solve a class of non-smooth constrained global optimization

Mohamed Rahal   orcid.org/0000-0003-4656-3426 ; Department of Mathematics, Ferhat Abbas Setif 1, University of Setif
Ziadi Abdelkader ; Department of Mathematics, Ferhat Abbas Setif 1, University of Setif
Ellaia Rachid ; Laboratory of Study and Research for Applied Mathematics, Mohammadia School of Engineers

 Puni tekst: engleski, pdf (765 KB) str. 289-314 preuzimanja: 233* citiraj APA 6th EditionRahal, M., Abdelkader, Z. i Rachid, E. (2019). Generating $\alpha$-dense curves in non-convex sets to solve a class of non-smooth constrained global optimization. Croatian Operational Research Review, 10 (2), 289-314. https://doi.org/10.17535/crorr.2019.0024 MLA 8th EditionRahal, Mohamed, et al. "Generating $\alpha$-dense curves in non-convex sets to solve a class of non-smooth constrained global optimization." Croatian Operational Research Review, vol. 10, br. 2, 2019, str. 289-314. https://doi.org/10.17535/crorr.2019.0024. Citirano 31.07.2021. Chicago 17th EditionRahal, Mohamed, Ziadi Abdelkader i Ellaia Rachid. "Generating $\alpha$-dense curves in non-convex sets to solve a class of non-smooth constrained global optimization." Croatian Operational Research Review 10, br. 2 (2019): 289-314. https://doi.org/10.17535/crorr.2019.0024 HarvardRahal, M., Abdelkader, Z., i Rachid, E. (2019). 'Generating $\alpha$-dense curves in non-convex sets to solve a class of non-smooth constrained global optimization', Croatian Operational Research Review, 10(2), str. 289-314. https://doi.org/10.17535/crorr.2019.0024 VancouverRahal M, Abdelkader Z, Rachid E. Generating $\alpha$-dense curves in non-convex sets to solve a class of non-smooth constrained global optimization. Croatian Operational Research Review [Internet]. 2019 [pristupljeno 31.07.2021.];10(2):289-314. https://doi.org/10.17535/crorr.2019.0024 IEEEM. Rahal, Z. Abdelkader i E. Rachid, "Generating $\alpha$-dense curves in non-convex sets to solve a class of non-smooth constrained global optimization", Croatian Operational Research Review, vol.10, br. 2, str. 289-314, 2019. [Online]. https://doi.org/10.17535/crorr.2019.0024

Sažetak

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.

Hrčak ID: 229888

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