{"product_id":"algebraic-and-geometric-ideas-in-the-theory-of-discrete-optimization-paperback-softback-9781611972436","title":"Algebraic and Geometric Ideas in the Theory of Discrete Optimization (Paperback \/ softback) 9781611972436","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eAlgebraic and Geometric Ideas in the Theory of Discrete Optimization\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cem\u003eA textbook for students in mathematics, computer science and OR that presents new techniques in the area of discrete optimization.\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eJesús A De Loera (Author), Raymond Hemmecke (Author), Matthias Koppe (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9781611972436\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003ePaperback \/ softback, published 30 December 2012\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e341 pages\u003cbr\u003e25.8 x 18.4 x 2.1 cm, 0.69 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003eIn recent years, many new techniques have emerged in the mathematical theory of discrete optimization that have proven to be effective in solving a number of hard problems. This book presents these recent advances, particularly those that arise from algebraic geometry, commutative algebra, convex and discrete geometry, generating functions, and other tools normally considered outside of the standard curriculum in optimization. These new techniques, all of which are presented with minimal prerequisites, provide a transition from linear to nonlinear discrete optimization. This book can be used as a textbook for advanced undergraduates or first-year graduate students in mathematics, computer science or operations research. It is also appropriate for mathematicians, engineers, and scientists engaged in computation who wish to gain a deeper understanding of how and why algorithms work.\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eList of figures\u003cbr\u003e List of tables\u003cbr\u003e List of algorithms\u003cbr\u003e Preface\u003cbr\u003e Part I. Established Tools of Discrete Optimization: 1. Tools from linear and convex optimization\u003cbr\u003e 2. Tools from the geometry of numbers and integer optimization\u003cbr\u003e Part II. Graver Basis Methods: 3. Graver bases\u003cbr\u003e 4. Graver bases for block-structured integer programs\u003cbr\u003e Part III. Generating Function Methods: 5. Introduction to generating functions\u003cbr\u003e 6. Decompositions of indicator functions of polyhedral\u003cbr\u003e 7. Barvinok's short rational generating functions\u003cbr\u003e 8. Global mixed-integer polynomial optimization via the summation method\u003cbr\u003e 9. Multicriteria integer linear optimization via Barvinok–Woods integer projection\u003cbr\u003e Part IV. Gröbner Basis Methods: 10. Computations with polynomials\u003cbr\u003e 11. Gröbner bases in integer programming\u003cbr\u003e Part V. Nullstellensatz and Positivstellensatz Relaxations: 12. The Nullstellensatz in discrete optimization\u003cbr\u003e 13. Positivity of polynomials and global optimization\u003cbr\u003e 14. Epilogue\u003cbr\u003e Bibliography\u003cbr\u003e Index.\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Miscellaneous items [\u003ca title=\"See our other books on Miscellaneous items\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Miscellaneous%20items%20%5BWZ%5D%22\"\u003eWZ\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"MP–SIA SIAM – Society for Industrial and Applied M","offers":[{"title":"Brand New","offer_id":52446331044120,"sku":"9781611972436","price":79.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/files\/9781611972436i.jpg?v=1785111087","url":"https:\/\/freshlyprintedbooks.co.uk\/products\/algebraic-and-geometric-ideas-in-the-theory-of-discrete-optimization-paperback-softback-9781611972436","provider":"Freshly Printed Books","version":"1.0","type":"link"}