Duality and approximation techniques are then covered, as are statistical estimation techniques. I recommend it as one of the best optimization textbooks that have appeared in the last years. LUO AND YU: AN INTRODUCTION TO CONVEX OPTIMIZATION FOR COMMUNICATIONS AND SIGNAL PROCESSING 1427 is not convex since the line segment joining any two distinct points is no longer on the unit sphere. A large body of literature is devoted to obtaining rates of convergence of specific procedures for various classes of convex optimization problems.
At the core of our approach are (i) A sequential convex optimization procedure, which penalizes collisions … ē] (mathematics) A convex set that has at least one interior point. On the other hand, our quantum lower bounds demonstrate that the quantum speedup … For teachers of convex optimization this book can be a gold mine of exercises.You can save your searches here and later view and run them again in "My saved searches".Full text views reflects the number of PDF downloads, PDFs sent to Google Drive, Dropbox and Kindle and HTML full text views for chapters in this book.Usage data cannot currently be displayed.Book summary views reflect the number of visits to the book and chapter landing pages. For example, the areas of convex surfaces and the volumes of any convex bodies are determined in this way. Convex optimization problems arise frequently in many different fields. This information should not be considered complete, up to date, and is not intended to be used in place of a visit, consultation, or advice of a legal, medical, or any other professional.The general theory of convex bodies and convex surfaces constitutes the so-called geometry of convex bodies. The focus of the book is on recognizing convex optimization problems and then finding the most appropriate technique for solving them. Convex bodies can be defined by a support function expressing the distance from the origin of coordinates to the support surface as a function of the outer normal to the convex body (that is, of a unit vector that is perpendicular to the support surface and directed toward that one of two half-spaces that is defined by this surface and which contains no points of the convex body). This makes it possible to solve many problems of convex bodies as follows: the problem is solved for convex polyhedrons, and then by going to the limit, the corresponding result is established for any convex body. However, I think that even the experienced researcher in the field has something to gain from reading this book: I have very much enjoyed the easy to follow presentation of many meaningful examples and suggestive interpretations meant to help the student's understanding penetrate beyond the surface of the formal description of the concepts and techniques. If a given optimization problem can be transformed to a convex equivalent, then this interpretive benefit is acquired. That is a powerful attraction: the ability to visualize geometry of an optimization problem. The body shown in Figure l,a is convex and that shown in Figure l,b is not. This data will be updated every 24 hours. A sphere, a cube, a spherical segment, or a half-space are examples of convex bodies. Any connected part of a boundary … This book provides a comprehensive introduction to the subject, and shows in detail how such problems can be solved numerically with great efficiency. This represents a quadratic improvement over the best-known classical algorithm. The concept of convex bodies naturally arises in the geometry of spaces of constant curvature.