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Convergence conditions of genetic algorithms

International Journal of Computer Mathematics, 1998
Genetic Algorithms (henceforth G.A.) have been used during recent years as a valid option to classical optimization methods, such as heuristic ones, specially in problems with huge cardinal searching space, very common in NP-Complete problems. The goal of this work is the study of the necessary conditions (measured as the optimum values for the G.A ...
D. Barrios, L. Malumbres, J. Ríos
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Conditions for the convergence of evolutionary algorithms

Journal of Systems Architecture, 2001
This paper presents a theoretical analysis of the convergence conditions for evolutionary algorithms. The necessary and sufficient conditions, necessary conditions, and sufficient conditions for the convergence of evolutionary algorithms to the global optima are derived, which describe their limiting behaviors. Their relationships are explored.
Jun He 0004, Xinghuo Yu 0001
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A Convergence Property for Conditional Expectation

open access: yesAnnals of Probability, 1989
Let (X,\({\mathcal B},\mu)\) be a probability space, \({\mathcal A}^ a \)subalgebra of \({\mathcal B}\), \[ L({\mathcal A},{\mathcal B})=\{f\in L^ 1({\mathcal B})| \exists H_ f\in L^ 1({\mathcal B}:\quad | f| \leq H_ f\quad a.e.\},\quad T(t)=| f-E(f| {\mathcal B})|, \] and let M(f) be the g.l.b. of ``functions'' in \(L^ 1({\mathcal B})\) which dominate
Cornea, Aurel, Loeb, Peter A.
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Convergence Conditions for Ascent Methods

SIAM Review, 1969
Liberal conditions on the steps of a “descent” method for finding extrema of a function are given; most known results are special cases.
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Convergence of Conditional Expectation Operators

Theory of Probability & Its Applications, 1964
Two concepts of convergence for nets of $\sigma $-rings are defined for every Orlicz space $\mathfrak{L}_M^ * $, which imply essential, respectively, stochastic convergence of the corresponding conditional expectations of any random variable in $\mathfrak{L}_M^ * $.
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A NECESSARY CONDITION FOR THE CONVERGENCE OF THE FOURIER TRANSFORM

KIBERNETYKA TA SYSTEMNYI ANALIZ
The authors show that the Fourier transform plays an important role in many applied problems of system analysis. Its properties are analyzed, which directly affect the efficiency of using the optimal decision theory in the problems. The necessary condition for the convergence of the Fourier transform is established, which provides a powerful tool for ...
Tovkach, R. V., Medvid, V. M.
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On the Necessity of the Conditional Lindeberg Condition for Normal Convergence of Martingales

Journal of Mathematical Sciences, 2002
It has been known that the conditional Lindeberg condition and the fact that the conditional variance of a martingale is equal to 1 imply the weak convergence of the martingale to the standard normal law. It was not known whether the conditional Lindeberg condition is necessary or not until \textit{A. G. Sholomitskij} [Theory Probab. Appl. 43, No.
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On the order conditions of fuzzy convergence classes

Fuzzy Sets and Systems, 2003
Studying convergence classes for completely distributive lattices (as in [\textit{G. Gierz}, \textit{K. H. Hofmann}, \textit{K. Keimel}, \textit{J. D. Lawson}, \textit{M. Mislove} and \textit{D. S. Scott}, A compendium of continuous lattices (Springer-Verlag, Berlin) (1980; Zbl 0452.06001)]) and, in particular, the relationship between the lim inf ...
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Types of conditional convergence

2005
Summary: The aim of this paper is to investigate relations between different types of conditional convergence. Results presented in this paper generalize theorems obtained by \textit{P. Fernandez} [Bol. Soc. Bras. Mat. 3, 13--16 (1972; Zbl 0344.60008)] and \textit{A. R. Padmanabhan} [Math. Jap. 15, 111--117 (1970; Zbl 0234.60038)].
Nowak, Wioletta, Zięba, Wiesław
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