Solving the continuous nonlinear resource allocation problem with an interior point method

TL;DR

This paper demonstrates that a primal-dual interior point method, leveraging sparsity alone, can efficiently solve continuous nonlinear resource allocation problems, outperforming specialized methods lacking algebraic structure.

Contribution

The paper introduces a closed-form Newton search direction for interior point methods based solely on sparsity, enhancing solution efficiency for generic resource allocation problems.

Findings

Interior point method outperforms specialized methods without algebraic structure

Closed-form Newton direction derived from sparsity alone

Method effective for general nonlinear resource allocation problems

Abstract

Resource allocation problems are usually solved with specialized methods exploiting their general sparsity and problem-specific algebraic structure. We show that the sparsity structure alone yields a closed-form Newton search direction for the generic primal-dual interior point method. Computational tests show that the interior point method consistently outperforms the best specialized methods when no additional algebraic structure is available.