Sparse solutions of optimal control via Newton method for under-determined systems

TL;DR

This paper explores a Newton method approach to find sparse, minimal--norm solutions for complex, non-convex optimal control problems, demonstrating a novel application of iterative Newton techniques.

Contribution

It introduces a new application of Newton methods to solve non-convex, non-smooth optimal control problems with sparse solutions.

Findings

Successful application of Newton method to under-determined nonlinear systems

Ability to find sparse, -norm minimal solutions

Potential for solving complex optimal control problems efficiently

Abstract

We focus on finding sparse and least-$\ell_1$-norm solutions for unconstrained nonlinear optimal control problems. Such optimization problems are non-convex and non-smooth, nevertheless recent versions of Newton method for under-determined equations can be applied successively for such problems.