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yo koya m a @ r k m a t h . r i k k yo. a c . j p ABSTRACT This paper proposes an algebraic approach for parametric optimization which can be utilized for various problems in signal processing and control. The approach exploits the relationship between the sum of roots and polynomial spectral factorization and solves parametric polynomial spectral factorization by means of the sum of roots and the theory of Gröbner basis. This enables us to express quantities such as the optimal cost in terms of parameters and the sum of roots. Furthermore an optimization method over parameters is suggested that makes use of the results from parametric polynomial spectral factorization and also employs quantifier elimination. The proposed approach is demonstrated on a numerical example of a particular control problem.

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