Algorithmic Procedures for Stochastic Optimization

摘要

For purposes of preliminary discussion, it is convenient to identify stochastic optimization problems with:\udfindxεRnthatminimizesz=E{f(x,ξ∼)}\udwhere ξ is a random N-vector with distribution function, P, f:Rn x RN → R U +∞ is a lower semicontinuous function, possibly convex, where dom f(.ξ) = x |f(x,ξ) is finite, corresponds to the set of acceptable choices for x when ξ is the observed value of the random vector ξ, and\udE{f(x,ξ∼)}=∫f(x,ξ)dp(ξ)