An algebraic geometry approach to nonlinear parametric optimization in control

2005/09/13 by Ioannis A. Fotiou, Philipp Rostalski, Fotiou, Ioannis A. +5
Computer Science · Mathematics · #Advanced Optimization Algorithms Research #Algebraic Geometry (math.AG) #FOS: Mathematics #Numerical methods for differential equations #Optimization and Control (math.OC) #Polynomial and algebraic computation #math.AG #math.OC

paper · pdf · doi:10.48550/arxiv.math/0509288

arxiv created 2005/09/13 · openalex publication_date 2005/09/13 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Related

• Optimization on linear matrix inequalities for polynomial systems control
• Polynomial Optimization with Applications to Stability Analysis and Control - Alternatives to Sum of Squares
• Solving systems of polynomial inequalities with algebraic geometry methods
• Minimizing Polynomial Functions
• On inverse optimal control via polynomial optimization