Graph-based algorithms for the efficient solution of a class of optimization problems

TL;DR

This paper introduces graph-based algorithms tailored for structured optimization problems like speed planning and dynamic programming, demonstrating superior performance over standard solvers through numerical experiments.

Contribution

The paper presents two novel numerical procedures for structured optimization problems, applicable to general and linear subcases, improving computational efficiency.

Findings

Algorithms outperform commercial solvers in experiments

Effective for speed planning and dynamic programming

Applicable to general and linear subcases

Abstract

In this paper, we address a class of specially structured problems that include speed planning, for mobile robots and robotic manipulators, and dynamic programming. We develop two new numerical procedures, that apply to the general case and to the linear subcase. With numerical experiments, we show that the proposed algorithms outperform generic commercial solvers.