Genericity In Polynomial Optimization

 69,99 €

 69,99 €
Description de l’éditeur
In full generality, minimizing a polynomial function over a closed semialgebraic set requires complex mathematical equations. This book explains recent developments from singularity theory and semialgebraic geometry for studying polynomial optimization problems. Classes of generic problems are defined in a simple and elegant manner by using only the two basic (and relatively simple) notions of Newton polyhedron and nondegeneracy conditions associated with a given polynomial optimization problem. These conditions are well known in singularity theory, however, they are rarely considered within the optimization community.
Explanations focus on critical points and tangencies of polynomial optimization, Hölderian error bounds for polynomial systems, Frank–Wolfetype theorem for polynomial programs and wellposedness in polynomial optimization. It then goes on to look at optimization for the different types of polynomials. Through this text graduate students, PhD students and researchers of mathematics will be provided with the knowledge necessary to use semialgebraic geometry in optimization.
,0SemiAlgebraic Geometry, Critical Points and Tangencies, Hölderian Error Bounds, Frank–Wolfe Type Theorem, Polynomial Optimization, Genericity, Compact SemiAlgebraic Sets, Noncompact Semialgebraic Sets, Convex Polynomial OptimizationThe book will complement what is already rather extensively covered in the existing recent books, like the ones of Jean Bernard Lasserre, Monique Laurent, and Murray Marshall