This paper presents a novel partially distributed outer approximation algorithm, named PaDOA, for solving a class of structured mixed integer convex programming 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 and to mixed-integer regression.

本文提出了一种新颖的局部分布式外部逼近算法PaDOA，用于将一类结构化混合整数凸规划问题求解为全局最优。对于具有可分离凸目标函数，仿射耦合约束和紧凑域的混合混合整数优化问题，提出的方案使用迭代外部逼近方法。PaDOA通过在解决大规模结构化混合整数线性规划问题与部分解耦的混合整数非线性规划子问题（包括更少的整数变量）之间交替进行。我们建立了在有限次数的迭代后PaDOA收敛到全局最小化器的条件，并通过将其应用于恒温控制负载和混合整数回归来验证这些属性。