Reducing transformation and global optimization

Guettal, Djaouida; Ziadi, Abdelkader

doi:10.1016/j.amc.2011.11.053

Cited by 5 publications

(3 citation statements)

References 18 publications

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“…The dimensionality reduction approach (DR) that we will present in our work, is different with the approach given above. It has been proposed and developed by Cherruault et al [1,5,24,26] and based on the approximation of an n variables of the objective function by a single variable function by using a continuous parametric curve α , defined from a real interval I onto the n-dimensional compact D and satisfying a property described by the definition given below. Such a function α is said to be a space-densifying-curve in D [23,25].…”

Section: The Dimensionality Reduction Methodsmentioning

confidence: 99%

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

Rahal

Ziadi

Ellaia

2019

Cro. Oper. Res. Rev.

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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 R n and Hölderian. The fundamental principle is to provide explicitly a parametric representation xi = i(t), 1 ≤ i ≤ n of α-dense curve α in the compact D, for t in an interval I of R, which allows to convert the initial problem to a one-dimensional Hölder 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 α of the curve α and the accuracy of attaining the optimal solution is given. Some concrete α-dense curves in a non-convex feasible region D are constructed. The numerical results show that the proposed approach is efficient.

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Section: The Dimensionality Reduction Methodsmentioning

confidence: 99%

“…Such a function α is said to be a space-densifying-curve in D [23,25]. However, the introduction of these α-dense curves has allowed analytical argumentation of certain dimensionality reduction methods in global optimization techniques [5,17,24,26,27].…”

Section: The Dimensionality Reduction Methodsmentioning

confidence: 99%

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

Rahal

Ziadi

Ellaia

2019

Cro. Oper. Res. Rev.

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“…Caratzoulas and Floudas [9] proposed novel convex underestimators for trigonometric functions. Recently, years univariate global optimization problems have attracted common attention because they arise in many real-life applications and the obtained results can be easily generalized to the multivariate case [7,8,11,14,15,16,27,29].…”

Section: Introductionmentioning

confidence: 99%