Stochastic Dynamic Cutting Plane for Multistage Stochastic Convex Programs

Cutting Planes for Multistage Stochastic Integer Programs

This paper addresses the problem of finding cutting planes for multi-stage stochastic integer programs.We give a general method for generating cutting planes for multi-stage stochastic integer programs basedon combining inequalities that are valid for the individual scenarios. We apply the method to generatecuts for a stochastic version of a dynamic knapsack problem and to stochasti...

Hierarchical Sparsity in Multistage Convex Stochastic Programs

Adaptive discretization of convex multistage stochastic programs

min x FI(x,ξ) := ∑ i∈I pi f (xi,ξi) s.t. gt(n)(x 1, . . . ,xn,ζn) ≤ 0, xn ∈ Xt(n), n ∈ N(I) f (x,ξ), gt(x,ξ) convex in x, Xt convex, t = 1, . . . ,T Notation ξi i ∈ I scenarios of stoch. process ξ ξn := ξi,t(n) ζn := (ξ1, . . . ,ξn) xi i ∈ I decision vector for scenario i xn := xi,t(n) pi i ∈ I scenario probabilities N(I) nodes of scenario tree defined by scenarios in I t(n) timestage of node n...

On Dynamic Decomposition of Multistage Stochastic Programs

It is well known that risk-averse multistage stochastic optimization problems are often not in the form of a dynamic stochastic program, i.e. are not dynamically decomposable. In this paper we demonstrate how some of these problems may be extended in such a way that they are accessible to dynamic algorithms. The key technique is a new recursive formulation for the Average Value-atRisk. To this ...

Convergent Cutting-Plane and Partial-Sampling Algorithm for Multistage Stochastic Linear Programs with Recourse

We propose an algorithm for multistage stochastic linear programs with recourse where random quantities in different stages are independent. The algorithm approximates successively expected recourse functions by building up valid cutting planes to support these functions from below. In each iteration, for the expected recourse function in each stage, one cutting plane is generated using the dua...