Convex and concave relaxations of implicit functions
Convex and concave relaxations of implicit functions
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隐函数的凸和凹松弛
DOI：
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
P. I. Barton
中科院分区：
文献类型：
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作者：
M. D. Stuber;Joseph K. Scott;P. I. Barton
当现实世界模型涉及到非线性平等约束时，使用缩小空间方法来解决非convex NLP的确定性算法。因（状态）变量作为独立（决策）变量的隐式函数，因此可以获得大幅度降低。约束和目标函数是自变量的隐式功能，可以通过固定点迭代来估计，依赖于最近开发的广义麦考米克松弛和基于麦考米克的算法的放松和亚级繁殖的宽松的想法。隐含的功能是使用这些想法的。保证了框架，有限的收敛到ε-最佳的全局解决方案。
A deterministic algorithm for solving nonconvex NLPs globally using a reduced-space approach is presented. These problems are encountered when real-world models are involved as nonlinear equality constraints and the decision variables include the state variables of the system. By solving the model equations for the dependent (state) variables as implicit functions of the independent (decision) variables, a significant reduction in dimensionality can be obtained. As a result, the inequality constraints and objective function are implicit functions of the independent variables, which can be estimated via a fixed-point iteration. Relying on the recently developed ideas of generalized McCormick relaxations and McCormick-based relaxations of algorithms and subgradient propagation, the development of McCormick relaxations of implicit functions is presented. Using these ideas, the reduced space, implicit optimization formulation can be relaxed. When applied within a branch-and-bound framework, finite convergence to ε-optimal global solutions is guaranteed.