Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Self Concordant Barriers For Convex Approximations Of Structured Convex Sets PDF full book. Access full book title Self Concordant Barriers For Convex Approximations Of Structured Convex Sets.
| Author | : Levent Tunçel |
| Publisher | : |
| Total Pages | : 30 |
| Release | : 2007 |
| Genre | : |
| ISBN | : |
| Author | : Yurii Nesterov |
| Publisher | : SIAM |
| Total Pages | : 414 |
| Release | : 1994-01-01 |
| Genre | : Mathematics |
| ISBN | : 9781611970791 |
Specialists working in the areas of optimization, mathematical programming, or control theory will find this book invaluable for studying interior-point methods for linear and quadratic programming, polynomial-time methods for nonlinear convex programming, and efficient computational methods for control problems and variational inequalities. A background in linear algebra and mathematical programming is necessary to understand the book. The detailed proofs and lack of "numerical examples" might suggest that the book is of limited value to the reader interested in the practical aspects of convex optimization, but nothing could be further from the truth. An entire chapter is devoted to potential reduction methods precisely because of their great efficiency in practice.
| Author | : Yurii Nesterov |
| Publisher | : |
| Total Pages | : 0 |
| Release | : 2006 |
| Genre | : |
| ISBN | : |
In this paper we develop a technique for constructing self-concordant barriers for convex cones. We start from a simple proof for a variant of standard result [1] on transformation of a v-self-concordant barrier for a set into a self-concordant barrier for its conic hull with parameter (3.08 Vv + 3.57)2. Further, we develop a convenient composition theorem for constructing barriers directly for convex cones. In particular, we can construct now good barriers for several interesting cones obtained as a conic hull of epigraph of a univariate function. This technique works for power functions, entropy, logarithm and exponent function, etc. It provides a background for development of polynomial-time methods for separable optimization problems. Thus, our abilities in constructing good barriers for convex sets and cones become now identical.
| Author | : Yurii Nesterov |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 270 |
| Release | : 2003-12-31 |
| Genre | : Mathematics |
| ISBN | : 9781402075537 |
It was in the middle of the 1980s, when the seminal paper by Kar markar opened a new epoch in nonlinear optimization. The importance of this paper, containing a new polynomial-time algorithm for linear op timization problems, was not only in its complexity bound. At that time, the most surprising feature of this algorithm was that the theoretical pre diction of its high efficiency was supported by excellent computational results. This unusual fact dramatically changed the style and direc tions of the research in nonlinear optimization. Thereafter it became more and more common that the new methods were provided with a complexity analysis, which was considered a better justification of their efficiency than computational experiments. In a new rapidly develop ing field, which got the name "polynomial-time interior-point methods", such a justification was obligatory. Afteralmost fifteen years of intensive research, the main results of this development started to appear in monographs [12, 14, 16, 17, 18, 19]. Approximately at that time the author was asked to prepare a new course on nonlinear optimization for graduate students. The idea was to create a course which would reflect the new developments in the field. Actually, this was a major challenge. At the time only the theory of interior-point methods for linear optimization was polished enough to be explained to students. The general theory of self-concordant functions had appeared in print only once in the form of research monograph [12].
| Author | : Y. Nesterov |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 253 |
| Release | : 2013-12-01 |
| Genre | : Mathematics |
| ISBN | : 144198853X |
It was in the middle of the 1980s, when the seminal paper by Kar markar opened a new epoch in nonlinear optimization. The importance of this paper, containing a new polynomial-time algorithm for linear op timization problems, was not only in its complexity bound. At that time, the most surprising feature of this algorithm was that the theoretical pre diction of its high efficiency was supported by excellent computational results. This unusual fact dramatically changed the style and direc tions of the research in nonlinear optimization. Thereafter it became more and more common that the new methods were provided with a complexity analysis, which was considered a better justification of their efficiency than computational experiments. In a new rapidly develop ing field, which got the name "polynomial-time interior-point methods", such a justification was obligatory. Afteralmost fifteen years of intensive research, the main results of this development started to appear in monographs [12, 14, 16, 17, 18, 19]. Approximately at that time the author was asked to prepare a new course on nonlinear optimization for graduate students. The idea was to create a course which would reflect the new developments in the field. Actually, this was a major challenge. At the time only the theory of interior-point methods for linear optimization was polished enough to be explained to students. The general theory of self-concordant functions had appeared in print only once in the form of research monograph [12].
| Author | : Yurii Nesterov |
| Publisher | : Springer |
| Total Pages | : 589 |
| Release | : 2018-11-19 |
| Genre | : Mathematics |
| ISBN | : 3319915789 |
This book provides a comprehensive, modern introduction to convex optimization, a field that is becoming increasingly important in applied mathematics, economics and finance, engineering, and computer science, notably in data science and machine learning. Written by a leading expert in the field, this book includes recent advances in the algorithmic theory of convex optimization, naturally complementing the existing literature. It contains a unified and rigorous presentation of the acceleration techniques for minimization schemes of first- and second-order. It provides readers with a full treatment of the smoothing technique, which has tremendously extended the abilities of gradient-type methods. Several powerful approaches in structural optimization, including optimization in relative scale and polynomial-time interior-point methods, are also discussed in detail. Researchers in theoretical optimization as well as professionals working on optimization problems will find this book very useful. It presents many successful examples of how to develop very fast specialized minimization algorithms. Based on the author’s lectures, it can naturally serve as the basis for introductory and advanced courses in convex optimization for students in engineering, economics, computer science and mathematics.
| Author | : Stephen P. Boyd |
| Publisher | : Cambridge University Press |
| Total Pages | : 744 |
| Release | : 2004-03-08 |
| Genre | : Business & Economics |
| ISBN | : 9780521833783 |
Convex optimization problems arise frequently in many different fields. This book provides a comprehensive introduction to the subject, and shows in detail how such problems can be solved numerically with great efficiency. The book begins with the basic elements of convex sets and functions, and then describes various classes of convex optimization problems. Duality and approximation techniques are then covered, as are statistical estimation techniques. Various geometrical problems are then presented, and there is detailed discussion of unconstrained and constrained minimization problems, and interior-point methods. The focus of the book is on recognizing convex optimization problems and then finding the most appropriate technique for solving them. It contains many worked examples and homework exercises and will appeal to students, researchers and practitioners in fields such as engineering, computer science, mathematics, statistics, finance and economics.
| Author | : Valeriu Soltan |
| Publisher | : World Scientific |
| Total Pages | : 416 |
| Release | : 2015-03-12 |
| Genre | : Mathematics |
| ISBN | : 9814656712 |
This book provides a systematic treatment of algebraic and topological properties of convex sets (possibly non-closed or unbounded) in the n-dimensional Euclidean space. Topics under consideration include general properties of convex sets and convex hulls, cones and conic hulls, polyhedral sets, the extreme structure, support and separation properties of convex sets.Lectures on Convex Sets is self-contained and unified in presentation. The book grew up out of various courses on geometry and convexity, taught by the author for more than a decade. It can be used as a textbook for graduate students and even ambitious undergraduates in mathematics, optimization, and operations research. It may also be viewed as a supplementary book for a course on convex geometry or convex analysis, or as a source for independent study of the subject, suitable for non-geometers.
| Author | : |
| Publisher | : World Scientific |
| Total Pages | : 1131 |
| Release | : |
| Genre | : |
| ISBN | : |
| Author | : Kurt M. Anstreicher |
| Publisher | : |
| Total Pages | : 12 |
| Release | : 1997 |
| Genre | : |
| ISBN | : |
