Accessibility Theorems

Kurt Marti
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Kurt Marti: University of Bundeswehr Munich

Chapter Chapter 11 in Optimization Under Stochastic Uncertainty, 2020, pp 187-194 from Springer

Abstract: Abstract The central topic in the next chapters is to find sufficient conditions concerning the feasible domain D, the objective function f, and the sequence ( p n : n ∈ ℕ 0 ) $$(p_n: n \in \mathbb {N}_0)$$ of mutation probability distributions guaranteeing the convergence of the corresponding random search procedure ( X n : n ∈ ℕ 0 ) $$(X_n: n \in \mathbb {N}_0)$$ , hence, f ( X n ) → inf x ∈ D f ( x ) P − a.s. , n → ∞ , for all starting points x 0 ∈ D . $$\displaystyle \begin{aligned} f(X_n) \rightarrow \inf \limits _{x \in D}f(x) \quad P-\mbox{a.s.}, \:n \rightarrow \infty , ~~ \mbox{for all starting points} ~ x_0 \in D. \end{aligned} $$

Date: 2020
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DOI: 10.1007/978-3-030-55662-4_11

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