000			02094 a2200241 4500
008			240831b |||||||| |||| 00| 0 eng d
020			_a9781470476366
082			_a516.35 THE
100			_aTheobald, Thorsten
245			_aReal algebraic geometry and optimization
260			_aRhode Island, Providence: _bAmerican Mathematical Society (AMS), _c2024.
300			_axv, 293p.: _bcol. ill.; pbk.: _c25cm.
440			_aGraduate Studies in Mathematics; Vol. 241
504			_aIncludes Bibliography, and Index.
520			_aThis book provides a comprehensive and user-friendly exploration of the tremendous recent developments that reveal the connections between real algebraic geometry and optimization, two subjects that were usually taught separately until the beginning of the 21st century. Real algebraic geometry studies the solutions of polynomial equations and polynomial inequalities over the real numbers. Real algebraic problems arise in many applications, including science and engineering, computer vision, robotics, and game theory. Optimization is concerned with minimizing or maximizing a given objective function over a feasible set. Presenting key ideas from classical and modern concepts in real algebraic geometry, this book develops related convex optimization techniques for polynomial optimization. The connection to optimization invites a computational view on real algebraic geometry and opens doors to applications. Intended as an introduction for students of mathematics or related fields at an advanced undergraduate or graduate level, this book serves as a valuable resource for researchers and practitioners. Each chapter is complemented by a collection of beneficial exercises, notes on references, and further reading. As a prerequisite, only some undergraduate algebra is required. https://bookstore.ams.org/view?ProductCode=GSM/241
650			_aGeometry
650			_aAlgebraic
650			_aMathematical optimization
650			_aPolynomials
650			_aSpectrahedra
650			_aCylindrical algebraic decomposition
942			_cTD _2ddc
999			_c60567 _d60567