Real algebraic geometry and optimization / Thorsten Theobald.

Format:

Book

Author/Creator:

Theobald, Thorsten, 1971- author.

Series:

Graduate studies in mathematics ; 1065-7339 v. 241.

Graduate studies in mathematics, 1065-7339 ; 241

Language:

English

Subjects (All):

Geometry, Algebraic.

Mathematical optimization.

Polynomials.

Physical Description:

xv, 293 pages : illustrations (some color) ; 27 cm.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, [2024]

Summary:

"The purpose of this book is to provide a comprehensive access to interesting and important ideas in the interplay of real algebraic geometry and optimization. Until the beginning of the 21st century, these disciplines were usually taught separately from each other. The developments since then have exhibited the fruitful connections, mutual dependencies and computational implications"--Introduction.

Contents:

Preface

Univariate real polynomials

From polyhedra to semialgebraic sets

The Tarski-Seidenberg principle and elimination of quantifiers

Cylindrical algebraic decomposition

Linear, semidefinite and conic optimization

Positive polynomials

Polynomial optimization

Spectrahedra

Stable and hyperbolic polynomials

Relative entropy methods in semialgebraic optimization.

Notes:

Includes bibliographical references and index.

ISBN:

9781470474317

147047431X

9781470476366

1470476363

OCLC:

1414381284