The approximation algorithm for solving a sort of non-smooth programming

Hou, Zai-En; Fu-jian, Duan

doi:10.1016/j.amc.2006.06.129

Cited by 1 publication

(1 citation statement)

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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%

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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