Section: Partnerships and Cooperations
Regional Initiatives

Grant CAMiSAdo (funded by PGMO).
Computer Algebra Methods for SemiAlgebraic programming
Participants: J. Berthomieu [contact], M. Safey El Din.
SemiAlgebraic Programming is the art of optimizing some quantity subject to semialgebraic constraints. The very basic and natural instance of semialgebraic 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 semialgebraic 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 semialgebraic set defined by the instantiated system? And when the number of solutions is finite, what is this maximum number of solutions? Hence SemiAlgebraic Programming encompasses a wide range of computational issues related to semialgebraic sets. It finds applications in many engineering sciences. Let us mention the few ones that we target in CAMiSAdo: Pathplanning optimization in robotics, Mobility properties of manipulators in mechanism design, Stability analysis for sensorbased controllers.