Stochastic Dynamic Cutting Plane for multistage stochastic convex programs

TL;DR

This paper presents StoDCuP, an extension of SDDP for multistage stochastic convex programs, incorporating lower affine functions for nonlinear components and proving its convergence, including an inexact variant.

Contribution

It introduces StoDCuP, a novel algorithm that extends SDDP by handling nonlinear functions and provides convergence proofs for both exact and inexact solutions.

Findings

StoDCuP converges almost surely for exact solutions.

An inexact variant also converges with vanishing errors.

The method effectively handles nonlinear cost and constraint functions.

Abstract

We introduce StoDCuP (Stochastic Dynamic Cutting Plane), an extension of the Stochastic Dual Dynamic Programming (SDDP) algorithm to solve multistage stochastic convex optimization problems. At each iteration, the algorithm builds lower affine functions not only for the cost-to-go functions, as SDDP does, but also for some or all nonlinear cost and constraint functions. We show the almost sure convergence of StoDCuP. We also introduce an inexact variant of StoDCuP where all subproblems are solved approximately (with bounded errors) and show the almost sure convergence of this variant for vanishing errors.