Partially Distributed Outer Approximation

TL;DR

This paper introduces PaDOA, a partially distributed outer approximation algorithm for solving structured mixed integer convex problems efficiently, with proven convergence to global optimality under certain conditions.

Contribution

The paper proposes a novel algorithm, PaDOA, that combines distributed and centralized optimization techniques for mixed integer convex problems, with convergence guarantees.

Findings

PaDOA converges to global minimizers after finite iterations.

The algorithm effectively solves large-scale structured MICP problems.

Application to thermostatically controlled loads demonstrates practical utility.

Abstract

This paper presents a novel partially distributed outer approximation algorithm, named PaDOA, for solving a class of structured mixed integer convex programming (MICP) problems to global optimality. The proposed scheme uses an iterative outer approximation method for coupled mixed integer optimization problems with separable convex objective functions, affine coupling constraints, and compact domain. PaDOA proceeds by alternating between solving large-scale structured mixed-integer linear programming problems and partially decoupled mixed-integer nonlinear programming subproblems that comprise much fewer integer variables. We establish conditions under which PaDOA converges to global minimizers after a finite number of iterations and verify these properties with an application to thermostatically controlled loads.