Modélisation d'algorithmes d'optimisation à stratégie aléatoire. (Modelling random search optimization algorithms) (Q1091274)

Proposed are two conceptual algorithms for extending results about almost certain convergence of stochastic algorithms for optimization described as follows. Let f be a map from the vector space E to the set of real numbers R; f is to be minimized; \(x^ 0\) is an arbitrary point of E and \((\xi^ k)\) a family of random vectors, if \(f(x^ k+\xi^ k)\geq f(x^ k)\) then \(x^{k+1}=x^ k\) or else \(x^{k+1}=x^ k+\xi^ k\). The inspiration for the two conceptual algorithms came from Polak's conceptual algorithm [see \textit{E. Polak}, ''Computational methods in optimization. A unified approach'' (1971; Zbl 0301.90040)] for deterministic search in optimization.