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Attraction of trajectories of finite-difference inclusions and stability of numerical methods of stochastic nonsmooth optimization. (English. Russian original) Zbl 0728.90079

Sov. Phys., Dokl. 35, No. 8, 709-711 (1990); translation from Dokl. Akad. Nauk SSSR 313, No. 6, 1373-1376 (1990).
Summary: Noise tolerance of many stochastic and non-smooth optimization algorithms is attributable to general properties of attraction of the trajectories of some finite-difference inclusions to neighborhoods of stationary sets. In this paper we present a general construction of the attraction domain of finite-difference inclusions, which leads to meaningful results in various applications and, in particular, produces unimprovable attractors of the trajectories of numerical nonsmooth optimization methods in the presence of noise. The main mathematical apparatus is the direct Lyapunov method.

MSC:

90C30 Nonlinear programming
90C15 Stochastic programming
65K05 Numerical mathematical programming methods
49J52 Nonsmooth analysis
90C31 Sensitivity, stability, parametric optimization
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