A practical, accessible guide to optimization problems with discrete or integer variables<br> <br> Integer Programming stands out from other textbooks by explaining in clear and simple terms how to construct custom-made algorithms or use existing commercial software to obtain optimal or near-optimal solutions for a variety of real-world problems, such as airline timetables, production line schedules, or electricity production on a regional or national scale.<br> <br> Incorporating recent developments that have made it possible to solve difficult optimization problems with greater accuracy, author Laurence A. Wolsey presents a number of state-of-the-art topics not covered in any other textbook. These include improved modeling, cutting plane theory and algorithms, heuristic methods, and branch-and-cut and integer programming decomposition algorithms. This self-contained text:<br> * Distinguishes between good and bad formulations in integer programming problems<br> * Applies lessons learned from easy integer programs to more difficult problems<br> * Demonstrates with applications theoretical and practical aspects of problem solving<br> * Includes useful notes and end-of-chapter exercises<br> * Offers tremendous flexibility for tailoring material to different needs<br> <br> Integer Programming is an ideal text for courses in integer/mathematical programming-whether in operations research, mathematics, engineering, or computer science departments. It is also a valuable reference for industrial users of integer programming and researchers who would like to keep up with advances in the field.
Built using the popular programming language, Python, SageMath is a useful open-source computer software that covers many aspects of mathematics and computer science by using mathematics libraries and a computer algebra system. Filling a gap in computer programming literature, this book features a unique introduction to SageMath as a programming language with a focus on learning computer programming, algorithms, and problem solving. This book focuses on developing a better understanding of the main programming concepts in SageMath, without requiring any programming background. This book also presents the mathematical functions on SageMath, such as the plots and Sage Interacts in order to present a better understanding of the programming concepts that are more interesting than classical "console applications." Topical coverage includes: computer science; computer programming; SageMath; Sage Cloud; Sage Interacts; computer algebra systems; input, processing, and output, variables, operators, and lists; Boolean expressions and relational operators; if statements; for loops and while loops; strings; functions and libraries; GUI programming and interacts; recursive functions and fractals; cryptography and Caesar Cipher; binary numbers; ASCII code; and sorting and searching.
Dynamic programming has long been applied to numerous areas in mat- matics, science, engineering, business, medicine, information systems, b- mathematics, arti?cial intelligence, among others. Applications of dynamic programming have increased as recent advances have been made in areas such as neural networks, data mining, soft computing, and other areas of com- tational intelligence. The value of dynamic programming formulations and means to obtain their computational solutions has never been greater. This book describes the use of dynamic programming as a computational tool to solve discrete optimization problems. (1) We ?rst formulate large classes of discrete optimization problems in dynamic programming terms, speci?cally by deriving the dynamic progr- ming functional equations (DPFEs) that solve these problems. A text-based language, gDPS, for expressing these DPFEs is introduced. gDPS may be regarded as a high-level speci?cation language, not a conventional procedural computer programming language, but which can be used to obtain numerical solutions. (2)Wethende?neandexaminepropertiesofBellmannets, aclassofPetri nets that serves both as a formal theoretical model of dynamic programming problems, and as an internal computer data structure representation of the DPFEs that solve these problems. (3)Wealsodescribethedesign, implementation, anduseofasoftwaretool, calledDP2PN2Solver, for solving DPFEs. DP2PN2Solver may be regarded as a program generator, whose input is a DPFE, expressed in the input spec- cation language gDPS and internally represented as a Bellman net, and whose output is its numerical solution that is produced indirectly by the generation of solver code, which when executed yields the desired solution."
' The authors bring together expertise from East and West to present an authoritative, thoroughly up-to-date and detailed treatment of work in this area. ' The International Statistical Review. ' As a survey, of what is available and which techniques show promise in further investigations, the book certainly provides what one could wish for.' ' What this reviewer enjoyed most is the technical virtuosity required, and generously present, in quite a few of the analyses. This is a book to have your Ph.D. student read, to show him what life is like. ' Mathematical Reviews, issue 88i ' In summary, this book competently fills a certain niche and will be interesting and provocative to probabilistically inclined statisticians who enjoy studying new and important phenomena. ' Journal of the American Statistical Association 86 , March 1991.
Understanding programming and programming languages requires knowledge of the underlying theoretical model. This book explores aspects of programming that are amenable to mathematical proof. The author describes a programming theory which is much simpler and more comprehensive than the current theories to date. In the theoretical model, a specification is just a boolean expression and refinement is just an ordinary implication. The author develops a practical and broad method for writing precise specifications and designing programs whose executions probably satisfy the specifications. Beginning with preparatory material in logic, numbers, sets, lists, functions and relations, the book advances further into program theory, the heart of the book. Subsequent chapters may be selected or omitted according to course emphasis. The text will be useful to students in courses on programming methodology or verification at the advanced undergraduate or beginning graduate level, as well as for software engineers in the field. All technical terms are explained and then demonstrated in the book wherever possible. No advanced mathematical knowledge or programming language is assumed. The book contains numerous exercises and worked-out solutions for specific exercises. Transparency masters and solutions for the remaining exercises are available from the author.
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