کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
7155532 1462622 2015 15 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Deterministic global optimization using space-filling curves and multiple estimates of Lipschitz and Hölder constants
موضوعات مرتبط
مهندسی و علوم پایه سایر رشته های مهندسی مهندسی مکانیک
پیش نمایش صفحه اول مقاله
Deterministic global optimization using space-filling curves and multiple estimates of Lipschitz and Hölder constants
چکیده انگلیسی
In this paper, the global optimization problem miny∈SF(y) with S being a hyperinterval in RN and F(y) satisfying the Lipschitz condition with an unknown Lipschitz constant is considered. It is supposed that the function F(y) can be multiextremal, non-differentiable, and given as a 'black-box'. To attack the problem, a new global optimization algorithm based on the following two ideas is proposed and studied both theoretically and numerically. First, the new algorithm uses numerical approximations to space-filling curves to reduce the original Lipschitz multi-dimensional problem to a univariate one satisfying the Hölder condition. Second, the algorithm at each iteration applies a new geometric technique working with a number of possible Hölder constants chosen from a set of values varying from zero to infinity showing so that ideas introduced in a popular DIRECT method can be used in the Hölder global optimization. Convergence conditions of the resulting deterministic global optimization method are established. Numerical experiments carried out on several hundreds of test functions show quite a promising performance of the new algorithm in comparison with its direct competitors.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Communications in Nonlinear Science and Numerical Simulation - Volume 23, Issues 1–3, June 2015, Pages 328-342
نویسندگان
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