Introducing the Adaptive Convex Enveloping

TL;DR

This paper introduces Adaptive Convex Enveloping, a new algorithm for efficiently solving convex dynamic programming problems with continuous states and actions, emphasizing convexity verification and computational speed.

Contribution

It provides conditions for convexity verification and presents a novel, accurate, and fast algorithm for convex dynamic programming, expanding tools for continuous state-action problems.

Findings

Algorithm is accurate and reliable.

Significantly faster than existing methods.

Effective for multivariate continuous problems.

Abstract

Convexity, though extremely important in mathematical programming, has not drawn enough attention in the field of dynamic programming. This paper gives conditions for verifying convexity of the cost-to-go functions, and introduces an accurate, fast and reliable algorithm for solving convex dynamic programs with multivariate continuous states and actions, called Adaptive Convex Enveloping. This is a short introduction of the core technique created and used in my dissertation, so it is less formal, and misses some parts, such as literature review and reference, compared to a full journal paper.