A new extension of Piyavskii’s method to Hölder functions of several variables

Rahal, Mohamed Ilyas; Ziadi, Abdelkader

doi:10.1016/j.amc.2007.07.067

Cited by 9 publications

(19 citation statements)

References 12 publications

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“…In this lower bound we merge the advantages of KBB and αBB. Let l 0 and l 1 be real valued functions defined in [13,15,29] by…”

Section: Advantages and Disadvantages Of Two Methodsmentioning

confidence: 99%

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New technique for solving univariate global optimization

Aaid¹,

Noui²,

Ouanes³

2017

Arch. Math. (Brno)

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“…In this lower bound we merge the advantages of KBB and αBB. Let l 0 and l 1 be real valued functions defined in [13,15,29] by…”

Section: Advantages and Disadvantages Of Two Methodsmentioning

confidence: 99%

“…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%

New technique for solving univariate global optimization

Aaid¹,

Noui²,

Ouanes³

2017

Arch. Math. (Brno)

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“…During the last recent years, numerous works have been realized concerning Lipschitz functions [7,8,15,21]. More recently, some works tackling less regular functions have appeared [4,10,12,17]. The global maximisation of both univariate and multivariate Hölder functions over respectively an interval of R and a hyper-rectangle of R n was studied for the first time by Gourdin et al [4].…”

Section: Introductionmentioning

confidence: 99%

“…In [17], we have proposed two algorithms of both univariate and multivariate unconstrained Hölder functions. The first one is a modification of the Piyavskii's algorithm for the univariate case.…”

Section: Introductionmentioning

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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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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“…D. [12], Rahal M. and Ziadi A. [13], processed the case of holderian functions by trying to elaborate a sequence to converge to the optimum; except that, here, obtaining a sequence, to converge to the optimum, is not so obvious.…”

Section: Introductionmentioning

confidence: 99%

Global Optimization of Multivariate Holderian Functions Using Overestimators

Yahyaoui¹,

Ammar²

2017

OALib

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This paper deals with the global optimization of several variables Holderian functions. An algorithm using a sequence of overestimators of a single variable objective function was developed converging to the maximum. Then by the use of α-dense curves, we show how to implement this algorithm in a multidimensional optimization problem. Finally, we validate the algorithm by testing it on some test functions.

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A new extension of Piyavskii’s method to Hölder functions of several variables

Cited by 9 publications

References 12 publications

New technique for solving univariate global optimization

New technique for solving univariate global optimization

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

Global Optimization of Multivariate Holderian Functions Using Overestimators

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