Success/Failure-Driven Random Direction Procedures

Kurt Marti
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Kurt Marti: University of Bundeswehr Munich

Chapter Chapter 16 in Optimization Under Stochastic Uncertainty, 2020, pp 279-325 from Springer

Abstract: Abstract In this section we consider a random direction procedure, cf. G.S. Tarasenko, based on a very simple step length control. At any iteration step n the step length 1n is chosen deterministically according to the following algorithm: ℓ 1 = ℓ > 0 ℓ n + 1 = γ 1 ℓ n in case of success at the n -th step γ 2 ℓ n in case of failure in the n -th step , where γ 1 > ℓ , γ 2 ∈ ( 0 , ℓ ) $$\displaystyle \begin{aligned} \begin{array}{rcl} \ell_1 &\displaystyle = &\displaystyle \ell > 0 \\ \ell_{n+1} &\displaystyle = &\displaystyle \left\{ \begin{array}{ll} \gamma_1 \ell_n &\displaystyle \text{in case of success at the }n\text{-th step} \\ \gamma_2 \ell_n &\displaystyle \text{in case of failure in the }n\text{-th step}, \end{array} \right. \\ \text{where} &\displaystyle &\displaystyle \gamma_1 > \ell , \gamma_2 \in (0, \ell) \end{array} \end{aligned} $$ are fixed parameters.

Date: 2020
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DOI: 10.1007/978-3-030-55662-4_16

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