{"product_id":"essential-mathematics-for-convex-optimization-hardback-9781009510523","title":"Essential Mathematics for Convex Optimization (Hardback) 9781009510523","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eEssential Mathematics for Convex Optimization\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cem\u003eA textbook that introduces both convex analysis and modern topics in optimization in a mathematically rigorous yet accessible way.\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eFatma Kılınç-Karzan (Author), Arkadi Nemirovski (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9781009510523, Cambridge University Press\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eHardback, published 26 June 2025\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e450 pages\u003cbr\u003e26.1 x 18.7 x 2.8 cm, 1.04 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cem\u003e\u003cfont size=\"3\"\u003e'This is a well-structured textbook on the mathematical foundations of convex optimization. It focuses on the structure of convex sets and functions, separation theorems, subgradients, and the theory of duality. The treatment is rigorous but readable, balancing clarity with depth.' Osman Güler, University of Maryland, Baltimore County\u003c\/font\u003e\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003eWith an emphasis on timeless essential mathematical background for optimization, this textbook provides a comprehensive and accessible introduction to convex optimization for students in applied mathematics, computer science, and engineering. Authored by two influential researchers, the book covers both convex analysis basics and modern topics such as conic programming, conic representations of convex sets, and cone-constrained convex problems, providing readers with a solid, up-to-date understanding of the field. By excluding modeling and algorithms, the authors are able to discuss the theoretical aspects in greater depth. Over 170 in-depth exercises provide hands-on experience with the theory, while more than 30 'Facts' and their accompanying proofs enhance approachability. Instructors will appreciate the appendices that cover all necessary background and the instructors-only solutions manual provided online. By the end of the book, readers will be well equipped to engage with state-of-the-art developments in optimization and its applications in decision-making and engineering.\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003ePreface\u003cbr\u003e Main notational conventions\u003cbr\u003e Part I. Convex Sets in Rn: From First Acquaintance to Linear Programming Duality: 1. First acquaintance with convex sets\u003cbr\u003e 2. Theorems of caratheodory, radon, and helly\u003cbr\u003e 3. Polyhedral representations and Fourier-Motzkin elimination\u003cbr\u003e 4. General theorem on alternative and linear programming duality\u003cbr\u003e 5. Exercises for Part I\u003cbr\u003e Part II. Separation Theorem, Extreme Points, Recessive Directions, and Geometry of Polyhedral Sets: 6. Separation theorem and geometry of convex sets\u003cbr\u003e 7. Geometry of polyhedral sets\u003cbr\u003e 8. Exercises for Part II\u003cbr\u003e Part III. Convex Functions: 9. First acquaintance with convex functions\u003cbr\u003e 10. How to detect convexity\u003cbr\u003e 11. Minima and maxima of convex functions\u003cbr\u003e 12. Subgradients\u003cbr\u003e 13. Legendre transform\u003cbr\u003e 14. Functions of eigenvalues of symmetric matrices\u003cbr\u003e 15. Exercises for Part III\u003cbr\u003e Part IV. Convex Programming, Lagrange Duality, Saddle Points: 16. Convex programming problems and convex theorem on alternative\u003cbr\u003e 17. Lagrange function and Lagrange duality\u003cbr\u003e 18. Convex programming in cone-constrained form\u003cbr\u003e 19. Optimality conditions in convex programming\u003cbr\u003e 20. Cone-convex functions: elementary calculus and examples\u003cbr\u003e 21. Mathematical programming optimality conditions\u003cbr\u003e 22. Saddle points\u003cbr\u003e 23. Exercises for Part IV\u003cbr\u003e Appendices.\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Optimization [\u003ca title=\"See our other books on Optimization\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Optimization%20%5BPBU%5D%22\"\u003ePBU\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Cambridge University Press","offers":[{"title":"Brand New","offer_id":52501203583256,"sku":"9781009510523","price":46.45,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/files\/9781009510523i.jpg?v=1786217017","url":"https:\/\/freshlyprintedbooks.co.uk\/products\/essential-mathematics-for-convex-optimization-hardback-9781009510523","provider":"Freshly Printed Books","version":"1.0","type":"link"}