序列凸化技术(SCM)及其在大系统优化技术中的应用

SEQUENTIAL CONVEXIFYING METHOD (SCM) WITH APPLICATION TO OPTIMIZATION AND CONTROL

在大系统稳态递阶优化与控制中,关联平衡法(IBM)是十分重要的方法。但有许多实际问题不能直接应用IBM。本文提出一种新的目标凸化方法——序列凸化技术(SCM),它可以对大部分不能应用IBM的问题进行凸化,使凸化后的问题可以用IBM来求解。与增广Lagrangian方法不同,SCM在凸化中保持了目标可分性,从而给分解带来很大的方便。本文证明了SCM的收敛性,给出了收敛速度的估界。并指出,对于具有凸目标(不必严格凸)的问题来说,SCM的收敛比可任意调节。

In the hierarchical optimization and control of large scale steady-state systems, the Interaction Balance Method (IBM) is of great importance. Unfortunately, however, many practical problems cannot be solved directly with IBM. This paper introduces a new objective-convexifying techinique Sequential Convexifying Method (SCM), which turns most of IBM unsolvable problems into solvable ones. Being different from the Augmented Lagrangian Method, SCM maintains the separability of the objective in the convexification, which has eased the task of decomposition significantly. The main idea of SCM is to approximate the original problem by a sequence of convex programming problems, the limit of the solution sequence approaches to the optimum solution of the original problem. A convergence proof of SCM as well as the estimation of the convergence rate is presented, and it is indicated that the convergence ratio of SCM can be made arbitrarily small in the case of convex problem (of course, strictly convex is not necessary).