Convergence of Stationary Random Search Methods for Positive Success Probability

Kurt Marti
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Kurt Marti: University of Bundeswehr Munich

Chapter Chapter 13 in Optimization Under Stochastic Uncertainty, 2020, pp 207-211 from Springer

Abstract: Abstract Let ( X n : n ∈ ℕ 0 ) $$(X_n:n\in \mathbb {N}_0)$$ be in this section—in the sense of Definition 9.3 —a stationary R-S-M with the mutation transition probability p. Let us now again pose the question on which conditions ( X n : n ∈ ℕ 0 ) $$(X_n:n\in \mathbb {N}_0)$$ converge, i.e. when does f ( X n ) → f ∗ P − a.s. $$\displaystyle f(X_n) \rightarrow f^{\ast } \qquad P-\mbox{a.s.} \qquad $$ apply to any starting point x 0 ∈ D?

Date: 2020
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DOI: 10.1007/978-3-030-55662-4_13

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