An algebraic geometry approach to nonlinear parametric optimization in control

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We present a method for nonlinear parametric optimization based on algebraic geometry. The problem to be studied, which arises in optimal control, is to minimize a polynomial function with parameters subject to semialgebraic constraints. The method uses Groebner bases computation in conjunction with the eigenvalue method for solving systems of polynomial equations. In this way, certain companion matrices are constructed off-line. Then, given the parameter value, an on-line algorithm is used to efficiently obtain the optimizer of the original optimization problem in real time.

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Optimization and Control, Algebraic Geometry

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http://salesiana.dossiersoluciones.com/handle/123456789/76326

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0509288
 http://arxiv.org/abs/math/0509288

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arXiv