Genericity In Polynomial Optimization
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A01=Ha Huy Vui
A01=Tien Son Pham
Author_Ha Huy Vui
Author_Tien Son Pham
Category=PBK
Category=PBT
Category=PBU
Compact Semi-Algebraic Sets
Convex Polynomial Optimization
Critical Points and Tangencies
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
Frank-Wolfe Type Theorem
FrankAcAEURA"Wolfe Type Theorem
Frank–Wolfe Type Theorem
Genericity
HAfA?lderian Error Bounds
Holderian Error Bounds
Hölderian Error Bounds
Noncompact Semialgebraic Sets
Polynomial Optimization
Semi-Algebraic Geometry
Product details
- ISBN 9781786342218
- Publication Date: 23 Feb 2017
- Publisher: World Scientific Europe Ltd
- Publication City/Country: GB
- Product Form: Hardback
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In full generality, minimizing a polynomial function over a closed semi-algebraic set requires complex mathematical equations. This book explains recent developments from singularity theory and semi-algebraic 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 non-degeneracy 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-Wolfe-type theorem for polynomial programs and well-posedness 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 semi-algebraic geometry in optimization.
