An algebraic geometry approach to nonlinear parametric optimization in control

Details An algebraic geometry approach to nonlinear parametric optimization in control An algebraic geometry approach to nonlinear parametric optimization in control

2005-09-13

arxiv.org/abs/math/0509288v1

Mathematics

Optimization and Control

Scientific paper

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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