Wednesday, 16:15 - 16:40 h, Room: H 0107

 

Natasa Krejic
Nonmonotone line search methods with variable sample sizes

Coauthor: Natasa Krklec

 

Abstract:
Nonmonotone line search methods for minimization of unconstrained objective functions in the form of mathematical expectation are considered. Nonmonotone schemes can improve the likelihood of finding a global minimizer and convergence speed. Sample Average Approximation - SAA method transforms the expectation objective function into a real-valued deterministic function using a large sample in each iteration. The main drawback of this approach is its cost. We will analyze a couple of nonmonotone line search strategies with variable sample sizes. Two measures of progress - lack of precision and functional decrease are calculated at each iteration. Based on this two measures a new sample size is determined. Additional safe guard rule is imposed to ensure the consistency of the linear models obtained with different samples. The rule we will present allows us to increase or decrease the sample size in each iteration until we reach some neighborhood of the solution. After that the maximal sample size is used so the variable sample size strategy generates the solution of the same quality as SAA method but with significantly smaller number of functional evaluations.

 

Talk 3 of the invited session Wed.3.H 0107
"Line-search strategies" [...]
Cluster 16
"Nonlinear programming" [...]

 

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