A multi-parametric programming approach for multilevel hierarchical and decentralised optimisation problems
A multi-parametric programming approach for multilevel hierarchical and decentralised optimisation problems
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DOI：
10.1007/s10287-007-0062-z
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发表时间：
2009-10
影响因子：
0.9
通讯作者：
Nuno P. Faísca;P. Saraiva;B. Rustem;E. Pistikopoulos
中科院分区：
文献类型：
--
作者：
Nuno P. Faísca;P. Saraiva;B. Rustem;E. Pistikopoulos
在本文中，我们概述的基础上，我们最近的发展多参数规划和控制理论的多层次和一般分散的多级问题的解决方案的一般全局优化策略。其核心思想是重铸每个优化子问题，目前在层次结构中，作为一个多参数规划问题，参数是属于其余子问题的优化变量。然后将多级问题转换为单级线性/凸优化问题。对于分散的系统，其中一个以上的优化问题是目前在每一级的层次结构，纳什均衡被认为是。一个三人动态优化问题，以说明数学的发展。
In this paper, we outline the foundations of a general global optimisation strategy for the solution of multilevel hierarchical and general decentralised multilevel problems, based on our recent developments on multi-parametric programming and control theory. The core idea is to recast each optimisation subproblem, present in the hierarchy, as a multi-parametric programming problem, with parameters being the optimisation variables belonging to the remaining subproblems. This then transforms the multilevel problem into single-level linear/convex optimisation problems. For decentralised systems, where more than one optimisation problem is present at each level of the hierarchy, Nash equilibrium is considered. A three person dynamic optimisation problem is presented to illustrate the mathematical developments.