Research on algorithms and applications of stochastic programming, the study of procedures for decision making under uncertainty over time, has been very active in recent years and deserves to be more widely known. This is the first book devoted to the full scale of applications of stochastic programming and also the first to provide access to publicly available algorithmic systems. The 32 contributed papers in this volume are written by leading stochastic programming specialists and reflect the high level of activity in recent years in research on algorithms and applications. The book introduces the power of stochastic programming to a wider audience and demonstrates the application areas where this approach is superior to other modeling approaches. Applications of Stochastic Programming consists of two parts. The first part presents papers describing publicly available stochastic programming systems that are currently operational. All the codes have been extensively tested and developed and will appeal to researchers and developers who want to make models without extensive programming and other implementation costs. The codes are a synopsis of the best systems available, with the requirement that they be user-friendly, ready to go, and publicly available. The second part of the book is a diverse collection of application papers in areas such as production, supply chain and scheduling, gaming, environmental and pollution control, financial modeling, telecommunications, and electricity. It contains the most complete collection of real applications using stochastic programming available in the literature. The papers show how leading researchers choose to treat randomness when making planning models, with an emphasis on modeling, data, and solution approaches.

The Sharpest Cut is written in honor of Manfred Padberg, who has made fundamental contributions to both the theoretical and computational sides of integer programming and combinatorial optimization. This outstanding collection presents recent results in these areas that are closely connected to Padberg's research. His deep commitment to the geometrical approach to combinatorial optimization can be felt throughout this volume; his search for increasingly better and computationally efficient cutting planes gave rise to its title. The peer-reviewed papers contained here are based on invited lectures given at a workshop held in October 2001 to celebrate Padberg's 60th birthday. Grouped by topic (packing, stable sets, and perfect graphs; polyhedral combinatorics; general polytopes; semidefinite programming; computation), many of the papers set out to solve challenges set forth in Padberg's work. The book also shows how Padberg's ideas on cutting planes have influenced modern commercial optimization software. In addition, the volume contains a short curriculum vitae, a personal account of Padberg's work by Laurence Wolsey, and an appendix with reflections from Egon Balas, Claude Berge, and Harold Kuhn. Manfred Padberg was Research Professor, Stern School of Business, New York University until 2002. Over the course of his career he received many honors for his work, including the Lanchester Prize, Dantzig Prize, and the John von Neuman Theory Prize. He has published six books and over 100 articles.

This compact book, through the simplifying perspective it presents, will take a reader who knows little of interior-point methods to within sight of the research frontier, developing key ideas that were over a decade in the making by numerous interior-point method researchers. It aims at developing a thorough understanding of the most general theory for interior-point methods, a class of algorithms for convex optimization problems. The study of these algorithms has dominated the continuous optimization literature for nearly 15 years. In that time, the theory has matured tremendously, but much of the literature is difficult to understand, even for specialists. By focusing only on essential elements of the theory and emphasizing the underlying geometry, A Mathematical View of Interior-Point Methods in Convex Optimization makes the theory accessible to a wide audience, allowing them to quickly develop a fundamental understanding of the material. The author begins with a general presentation of material pertinent to continuous optimization theory, phrased so as to be readily applicable in developing interior-point method theory. This presentation is written in such a way that even motivated Ph.D. students who have never had a course on continuous optimization can gain sufficient intuition to fully understand the deeper theory that follows. Renegar continues by developing the basic interior-point method theory, with emphasis on motivation and intuition. In the final chapter, he focuses on the relations between interior-point methods and duality theory, including a self-contained introduction to classical duality theory for conic programming; an exploration of symmetric cones; and the development of the general theory of primal-dual algorithms for solving conic programming optimization problems. Rather than attempting to be encyclopedic, A Mathematical View of Interior-Point Methods in Convex Optimization gives the reader a solid understanding of the core concepts and relations, the kind of understanding that stays with a reader long after the book is finished.

Here is a book devoted to well-structured and thus efficiently solvable convex optimization problems, with emphasis on conic quadratic and semidefinite programming. The authors present the basic theory underlying these problems as well as their numerous applications in engineering, including synthesis of filters, Lyapunov stability analysis, and structural design. The authors also discuss the complexity issues and provide an overview of the basic theory of state-of-the-art polynomial time interior point methods for linear, conic quadratic, and semidefinite programming. The book's focus on well-structured convex problems in conic form allows for unified theoretical and algorithmical treatment of a wide spectrum of important optimization problems arising in applications. Lectures on Modern Convex Optimization presents and analyzes numerous engineering models, illustrating the wide spectrum of potential applications of the new theoretical and algorithmical techniques emerging from the significant progress taking place in convex optimization. It is hoped that the information provided here will serve to promote the use of these techniques in engineering practice. The book develops a kind of "algorithmic calculus" of convex problems, which can be posed as conic quadratic and semidefinite programs. This calculus can be viewed as a "computationally tractable" version of the standard convex analysis.

This is the first comprehensive reference on trust-region methods, a class of numerical algorithms for the solution of nonlinear convex optimization methods. Its unified treatment covers both unconstrained and constrained problems and reviews a large part of the specialized literature on the subject. It also provides an up-to-date view of numerical optimization.

Written primarily for postgraduates and researchers, the book features an extensive commented bibliography, which contains more than 1000 references by over 750 authors. The book also contains several practical comments and an entire chapter devoted to software and implementation issues. Its many illustrations, including nearly 100 figures, balance the formal and intuitive treatment of the presented topics.