ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

17. Control Theory and Optimization

1991 MS Classification: 90, 65, 60 Norkin, Vladimir, Glushkov Institute of Cybernetics, Kiev, Ukraine Stochastic optimization of discontinuous functions A problem of minimization of a semicontinuous function F over a compact set X ⊂ R^{n} is approximated by a sequence of stochastic optimization problems min_{x∈X}[F_{α}(x) = E_{y_{α}}F (x+y_{α})] with expectation functions F_{α}(x) epi-converging to F as approximation parameter α ⟶ 0. For a discontinuous function F an extended mollifier subdifferential is introduced in a compact space of pairs \overline{R^{n}} = \{(n, ρ)| n ∈ R^{n}, ∥n∥ = 1, 0 ≤ ρ ≤ +∞\} and necessary optimality conditions are formulated. To find local minimums of F_{α} on X nonconvex stochastic optimization technique is applied. Part of these results is a joint work with Yu. Ermoliev and R. Wets. References: Yu. M. Ermoliev, V. I. Norkin and R. J-B. Wets, The minimization of semi-continuous functions: Mollifier subgradients, SIAM J. Contr. and Opt. , 1 (1995), 149-167. Yu. M. Ermoliev and V. I. Norkin, On nonsmooth and discontinuous problems of stochastic systems optimization, European J. of Oper. Res. 101 (1997), 230-244.