Optimization on fractal sets
نویسندگان
چکیده
In the sequel, we outline necessary and sufficient condition to existence of extremas a function on self-similar set, describe discrete gradient algorithm find extrema.
منابع مشابه
Expectations on fractal sets
Using fractal self-similarity and functional-expectation relations, the classical theory of box integrals—being expectations on unit hypercubes—is extended to a class of fractal “string-generated Cantor sets” (SCSs) embedded in unit hypercubes of arbitrary dimension. Motivated by laboratory studies on the distribution of brain synapses, these SCSs were designed for dimensional freedom—a suitabl...
متن کاملFrom Fractal Groups to Fractal Sets
3 Self-similar sets and (semi)group actions 8 3. 11 Finitely presented dynamical systems and semi-Markovian spaces 57 12 Spectra of Schreier graphs and Hecke type operators 59 12. 15 Ergodic Theorems and uniform distribution 72 16 Entropy of a set of non-commuting transformations 76 1 Introduction The idea of self-similarity is one of the most fundamental in the modern mathematics. The notion o...
متن کاملQuasi-fractal sets in space
Let a be a positive real number, a < 1/2. A standard construction of a self-similar Cantor set in the plane starts with the unit square [0, 1]× [0, 1], replaces it with the four corner squares with sidelength a, then replaces each of those squares with their four corner squares of sidelength a, and so on. At the nth stage one has 4 squares with sidelength a, and the resulting Cantor set has Hau...
متن کاملStatistically Self - Similar Fractal Sets
In the present paper we define statistically self-similar sets, and, using a modification of method described in [2], [3], find a Hausdorff dimension of a statistically self-similar set.
متن کاملAdaptive FMM for fractal sets
N 2 interactions amongN points orN variables appears in the boundary element methods, problems involving radial basis functions or in probability theory to describe dense covariance matrices. The fast multipole formulation introduced by Greengard and Rokhlin approximates a matrixvector multiplication of the above form with desired accuracy in O(N) time. Several works have extended the algorithm...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Optimization Letters
سال: 2021
ISSN: ['1862-4480', '1862-4472']
DOI: https://doi.org/10.1007/s11590-020-01689-7