Section: Partnerships and Cooperations

Regional Initiatives

Grant CAMiSAdo (funded by PGMO).

Computer Algebra Methods for Semi-Algebraic programming

Participants: J. Berthomieu [contact], M. Safey El Din.

Semi-Algebraic Programming is the art of optimizing some quantity subject to semi-algebraic constraints. The very basic and natural instance of semi-algebraic programming is the problem of optimizating a polynomial function subject to polynomial inequalities and is known as the polynomial optimization problem (POP). More general instances of semi-algebraic programming are as follows: given a system of polynomial equations/inequalities depending on parameters, what are the parameters’ values which maximize the dimension of the semi-algebraic set defined by the instantiated system? And when the number of solutions is finite, what is this maximum number of solutions? Hence Semi-Algebraic Programming encompasses a wide range of computational issues related to semi-algebraic sets. It finds applications in many engineering sciences. Let us mention the few ones that we target in CAMiSAdo: Path-planning optimization in robotics, Mobility properties of manipulators in mechanism design, Stability analysis for sensor-based controllers.