{"product_id":"linear-and-convex-optimization-isbn-9781119664048","title":"Linear and Convex Optimization","description":"\u003cp\u003e\u003cb\u003eDiscover the practical impacts of current methods of optimization with this approachable, one-stop resource\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003ci\u003eLinear and Convex Optimization: A Mathematical Approach\u003c\/i\u003e delivers a concise and unified treatment of optimization with a focus on developing insights in problem structure, modeling, and algorithms. Convex optimization problems are covered in detail because of their many applications and the fast algorithms that have been developed to solve them. \u003c\/p\u003e \u003cp\u003eExperienced researcher and undergraduate teacher Mike Veatch presents the main algorithms used in linear, integer, and convex optimization in a mathematical style with an emphasis on what makes a class of problems practically solvable and developing insight into algorithms geometrically. Principles of algorithm design and the speed of algorithms are discussed in detail, requiring no background in algorithms.\u003c\/p\u003e \u003cp\u003eThe book offers a breadth of recent applications to demonstrate the many areas in which optimization is successfully and frequently used, while the process of formulating optimization problems is addressed throughout. \u003c\/p\u003e \u003cp\u003e\u003ci\u003eLinear and Convex Optimization\u003c\/i\u003e contains a wide variety of features, including:\u003c\/p\u003e \u003cul\u003e \u003cli\u003eCoverage of current methods in optimization in a style and level that remains appealing and accessible for mathematically trained undergraduates\u003c\/li\u003e \u003cli\u003eEnhanced insights into a few algorithms, instead of presenting many algorithms in cursory fashion\u003c\/li\u003e \u003cli\u003eAn emphasis on the formulation of large, data-driven optimization problems\u003c\/li\u003e \u003cli\u003eInclusion of linear, integer, and convex optimization, covering many practically solvable problems using algorithms that share many of the same concepts\u003c\/li\u003e \u003cli\u003ePresentation of a broad range of applications to fields like online marketing, disaster response, humanitarian development, public sector planning, health delivery, manufacturing, and supply chain management\u003c\/li\u003e \u003c\/ul\u003e \u003cp\u003eIdeal for upper level undergraduate mathematics majors with an interest in practical applications of mathematics, this book will also appeal to business, economics, computer science, and operations research majors with at least two years of mathematics training.\u003cbr\u003e\u003cbr\u003eSoftware to accompany the text can be found here: \u003ca href=\"https:\/\/urldefense.com\/v3\/__https:\/www.gordon.edu\/michaelveatch\/optimization__;!!N11eV2iwtfs!62z2-kUgY15p8SDzObjque7UxKYjjt3HiPJJJPd7YLp2khRtq9Csaz1RahXzpeo$\"\u003ehttps:\/\/www.gordon.edu\/michaelveatch\/optimization\u003c\/a\u003e\u003c\/p\u003e \u003cp\u003ePreface xi\u003c\/p\u003e \u003cp\u003eAbout the Companion Website xvii\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Introduction to Optimization Modeling 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Who Uses Optimization? 1\u003c\/p\u003e \u003cp\u003e1.2 Sending Aid to a Disaster 3\u003c\/p\u003e \u003cp\u003e1.3 Optimization Terminology 9\u003c\/p\u003e \u003cp\u003e1.4 Classes of Mathematical Programs 11\u003c\/p\u003e \u003cp\u003eProblems 16\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Linear Programming Models 19\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Resource Allocation 19\u003c\/p\u003e \u003cp\u003e2.2 Purchasing and Blending 23\u003c\/p\u003e \u003cp\u003e2.3 Workforce Scheduling 29\u003c\/p\u003e \u003cp\u003e2.4 Multiperiod Problems 30\u003c\/p\u003e \u003cp\u003e2.5 Modeling Constraints 34\u003c\/p\u003e \u003cp\u003e2.6 Network Flow 36\u003c\/p\u003e \u003cp\u003eProblems 44\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Linear Programming Formulations 55\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Changing Form 55\u003c\/p\u003e \u003cp\u003e3.2 Linearization of Piecewise Linear Functions 57\u003c\/p\u003e \u003cp\u003e3.3 Dynamic Programming 62\u003c\/p\u003e \u003cp\u003eProblems 66\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Integer Programming Models 71\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Quantitative Variables and Fixed Costs 72\u003c\/p\u003e \u003cp\u003e4.2 Set Covering 74\u003c\/p\u003e \u003cp\u003e4.3 Logical Constraints and Piecewise Linear Functions 77\u003c\/p\u003e \u003cp\u003e4.4 Additional Applications 81\u003c\/p\u003e \u003cp\u003e4.5 Traveling Salesperson and Cutting Stock Problems 86\u003c\/p\u003e \u003cp\u003eProblems 90\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Iterative Search Algorithms 99\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Iterative Search and Constructive Algorithms 100\u003c\/p\u003e \u003cp\u003e5.2 Improving Directions and Optimality 106\u003c\/p\u003e \u003cp\u003e5.3 Computational Complexity and Correctness 112\u003c\/p\u003e \u003cp\u003eProblems 116\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Convexity 121\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Convex Sets 122\u003c\/p\u003e \u003cp\u003e6.2 Convex and Concave Functions 127\u003c\/p\u003e \u003cp\u003eProblems 131\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Geometry and Algebra of LPs 133\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Extreme Points and Basic Feasible Solutions 134\u003c\/p\u003e \u003cp\u003e7.2 Optimality of Extreme Points 137\u003c\/p\u003e \u003cp\u003e7.3 Linear Programs in Canonical Form 140\u003c\/p\u003e \u003cp\u003e7.4 Optimality Conditions 145\u003c\/p\u003e \u003cp\u003e7.5 Optimality for General Polyhedra 146\u003c\/p\u003e \u003cp\u003eProblems 149\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Duality Theory 153\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 Dual of a Linear Program 153\u003c\/p\u003e \u003cp\u003e8.2 Duality Theorems 158\u003c\/p\u003e \u003cp\u003e8.3 Complementary Slackness 162\u003c\/p\u003e \u003cp\u003e8.4 Lagrangian Duality 164\u003c\/p\u003e \u003cp\u003e8.5 Farkas’ Lemma and Optimality 167\u003c\/p\u003e \u003cp\u003eProblems 170\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 Simplex Method 173\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1 Simplex Method From a Known Feasible Solution 174\u003c\/p\u003e \u003cp\u003e9.2 Degeneracy and Correctness 183\u003c\/p\u003e \u003cp\u003e9.3 Finding an Initial Feasible Solution 186\u003c\/p\u003e \u003cp\u003e9.4 Computational Strategies and Speed 192\u003c\/p\u003e \u003cp\u003eProblems 200\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10 Sensitivity Analysis 203\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e10.1 Graphical Sensitivity Analysis 204\u003c\/p\u003e \u003cp\u003e10.2 Shadow Prices and Reduced Costs 208\u003c\/p\u003e \u003cp\u003e10.3 Economic Interpretation of the Dual 219\u003c\/p\u003e \u003cp\u003eProblems 221\u003c\/p\u003e \u003cp\u003e\u003cb\u003e11 Algorithmic Applications of Duality 225\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e11.1 Dual Simplex Method 226\u003c\/p\u003e \u003cp\u003e11.2 Network Simplex Method 234\u003c\/p\u003e \u003cp\u003e11.3 Primal-Dual Interior Point Method 246\u003c\/p\u003e \u003cp\u003eProblems 256\u003c\/p\u003e \u003cp\u003e\u003cb\u003e12 Integer Programming Theory 261\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e12.1 Linear Programming Relaxations 262\u003c\/p\u003e \u003cp\u003e12.2 Strong Formulations 263\u003c\/p\u003e \u003cp\u003e12.3 Unimodular Matrices 269\u003c\/p\u003e \u003cp\u003eProblems 272\u003c\/p\u003e \u003cp\u003e\u003cb\u003e13 Integer Programming Algorithms 275\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e13.1 Branch and Bound Methods 275\u003c\/p\u003e \u003cp\u003e13.2 Cutting Plane Methods 284\u003c\/p\u003e \u003cp\u003eProblems 293\u003c\/p\u003e \u003cp\u003e\u003cb\u003e14 Convex Programming: Optimality Conditions 297\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e14.1 KKT Optimality Conditions 297\u003c\/p\u003e \u003cp\u003e14.2 Lagrangian Duality 306\u003c\/p\u003e \u003cp\u003eProblems 312\u003c\/p\u003e \u003cp\u003e\u003cb\u003e15 Convex Programming: Algorithms 317\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e15.1 Convex Optimization Models 320\u003c\/p\u003e \u003cp\u003e15.2 Separable Programs 323\u003c\/p\u003e \u003cp\u003e15.3 Unconstrained Optimization 325\u003c\/p\u003e \u003cp\u003e15.4 Quadratic Programming 329\u003c\/p\u003e \u003cp\u003e15.5 Primal-dual Interior Point Method 331\u003c\/p\u003e \u003cp\u003eProblems 339\u003c\/p\u003e \u003cp\u003e\u003cb\u003eA Linear Algebra and Calculus Review 343\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eA.1 Sets and Other Notation 343\u003c\/p\u003e \u003cp\u003eA.2 Matrix and Vector Notation 343\u003c\/p\u003e \u003cp\u003eA.3 Matrix Operations 345\u003c\/p\u003e \u003cp\u003eA.4 Matrix Inverses 347\u003c\/p\u003e \u003cp\u003eA.5 Systems of Linear Equations 348\u003c\/p\u003e \u003cp\u003eA.6 Linear Independence and Rank 350\u003c\/p\u003e \u003cp\u003eA.7 Quadratic Forms and Eigenvalues 351\u003c\/p\u003e \u003cp\u003eA.8 Derivatives and Convexity 352\u003c\/p\u003e \u003cp\u003eBibliography 355\u003c\/p\u003e \u003cp\u003eIndex 361\u003c\/p\u003e  \u003cp\u003e\u003cb\u003eMichael H. Veatch, PhD,\u003c\/b\u003e is Professor of Mathematics at Gordon College, in Wenham, Massachusetts, United States. He obtained his PhD in Operations Research from the Massachusetts Institute of Technology in Cambridge, MA and has been working in operations research for 40 years.   \u003c\/p\u003e\u003cp\u003e\u003cb\u003eDiscover the practical impacts of current methods of optimization with this approachable, one-stop resource\u003c\/b\u003e \u003c\/p\u003e\u003cp\u003e\u003ci\u003eLinear and Convex Optimization: A Mathematical Approach\u003c\/i\u003e delivers a concise and unified treatment of optimization with a focus on developing insights in problem structure, modeling, and algorithms. Convex optimization problems are covered in detail because of their many applications and the fast algorithms that have been developed to solve them. \u003c\/p\u003e\u003cp\u003eExperienced researcher and undergraduate instructor Mike Veatch presents the main algorithms used in linear, integer, and convex optimization in a mathematical style with an emphasis on what makes a class of problems practically solvable and developing insight into algorithms geometrically. Principles of algorithm design and the speed of algorithms are discussed in detail, requiring no background in algorithms. \u003c\/p\u003e\u003cp\u003eThe book offers a breadth of recent applications to demonstrate the many areas in which optimization is successfully and frequently used, while the process of formulating optimization problems is addressed throughout. \u003c\/p\u003e\u003cp\u003e\u003ci\u003eLinear and Convex Optimization\u003c\/i\u003e contains a wide variety of features, including: \u003c\/p\u003e\u003cul\u003e \u003cli\u003eCoverage of current methods in optimization in a style and level that remains appealing and accessible for mathematically trained undergraduates\u003c\/li\u003e \u003cli\u003eEnhanced insights into a few algorithms, instead of presenting many algorithms in cursory fashion\u003c\/li\u003e \u003cli\u003eAn emphasis on the formulation of large, data-driven optimization problems\u003c\/li\u003e \u003cli\u003eInclusion of linear, integer, and convex optimization, covering many practically solvable problems using algorithms that share many of the same concepts\u003c\/li\u003e \u003cli\u003ePresentation of a broad range of applications to fields like online marketing, disaster response, humanitarian development, public sector planning, health delivery, manufacturing, and supply chain management\u003c\/li\u003e \u003c\/ul\u003e \u003cp\u003eIdeal for upper level undergraduate mathematics majors with an interest in practical applications of mathematics, this book will also appeal to business, economics, computer science, and operations research majors with at least two years of mathematics training.\u003c\/p\u003e","brand":"Wiley","offers":[{"title":"Default Title","offer_id":47989531279589,"sku":"NP9781119664048","price":133.95,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/1842\/7735\/files\/9781119664048.jpg?v=1761784485","url":"https:\/\/k12savings.com\/products\/linear-and-convex-optimization-isbn-9781119664048","provider":"K12savings","version":"1.0","type":"link"}