On the Convergence of Primal-dual Interior Point Methods with Wide Neighborhoods
Author: Levent Tuncel
Publisher:
Published: 1992
Total Pages: 64
ISBN-13:
DOWNLOAD EBOOKPosts
Primal-Dual Interior-Point Methods
Author: Stephen J. Wright
Publisher: SIAM
Published: 1997-01-01
Total Pages: 293
ISBN-13: 089871382X
DOWNLOAD EBOOKPresents the major primal-dual algorithms for linear programming. A thorough, straightforward description of the theoretical properties of these methods.
Primal-dual Interior-Point Methods
Author: Stephen J. Wright
Publisher: SIAM
Published: 1997-01-01
Total Pages: 309
ISBN-13: 9781611971453
DOWNLOAD EBOOKIn the past decade, primal-dual algorithms have emerged as the most important and useful algorithms from the interior-point class. This book presents the major primal-dual algorithms for linear programming in straightforward terms. A thorough description of the theoretical properties of these methods is given, as are a discussion of practical and computational aspects and a summary of current software. This is an excellent, timely, and well-written work. The major primal-dual algorithms covered in this book are path-following algorithms (short- and long-step, predictor-corrector), potential-reduction algorithms, and infeasible-interior-point algorithms. A unified treatment of superlinear convergence, finite termination, and detection of infeasible problems is presented. Issues relevant to practical implementation are also discussed, including sparse linear algebra and a complete specification of Mehrotra's predictor-corrector algorithm. Also treated are extensions of primal-dual algorithms to more general problems such as monotone complementarity, semidefinite programming, and general convex programming problems.
Arc-Search Techniques for Interior-Point Methods
Author: Yaguang Yang
Publisher: CRC Press
Published: 2020-11-26
Total Pages: 306
ISBN-13: 1000220133
DOWNLOAD EBOOKThis book discusses an important area of numerical optimization, called interior-point method. This topic has been popular since the 1980s when people gradually realized that all simplex algorithms were not convergent in polynomial time and many interior-point algorithms could be proved to converge in polynomial time. However, for a long time, there was a noticeable gap between theoretical polynomial bounds of the interior-point algorithms and efficiency of these algorithms. Strategies that were important to the computational efficiency became barriers in the proof of good polynomial bounds. The more the strategies were used in algorithms, the worse the polynomial bounds became. To further exacerbate the problem, Mehrotra's predictor-corrector (MPC) algorithm (the most popular and efficient interior-point algorithm until recently) uses all good strategies and fails to prove the convergence. Therefore, MPC does not have polynomiality, a critical issue with the simplex method. This book discusses recent developments that resolves the dilemma. It has three major parts. The first, including Chapters 1, 2, 3, and 4, presents some of the most important algorithms during the development of the interior-point method around the 1990s, most of them are widely known. The main purpose of this part is to explain the dilemma described above by analyzing these algorithms' polynomial bounds and summarizing the computational experience associated with them. The second part, including Chapters 5, 6, 7, and 8, describes how to solve the dilemma step-by-step using arc-search techniques. At the end of this part, a very efficient algorithm with the lowest polynomial bound is presented. The last part, including Chapters 9, 10, 11, and 12, extends arc-search techniques to some more general problems, such as convex quadratic programming, linear complementarity problem, and semi-definite programming.
Asymptotic Behavior of Interior-point Methods
Author: Levent Tuncel
Publisher:
Published: 1993
Total Pages: 274
ISBN-13:
DOWNLOAD EBOOKOn the Convergence of Interior-Point Methods to the Center of the Solution Set in Linear Programming
Author:
Publisher:
Published: 1991
Total Pages: 15
ISBN-13:
DOWNLOAD EBOOKThe notion of the central path plays an important role in the convergence analysis of interior-point methods. Many interior-point algorithms have been developed based on the principle of following the central path, either closely or otherwise. However, whether such algorithms actually converge to the center of the solution set has remained an open question. In this paper, we demonstrate that under mild conditions, when the iteration sequence generated by a primal-dual interior-point method converges, it converges to the center of the solution set.
Interior-point Polynomial Algorithms in Convex Programming
Author: Yurii Nesterov
Publisher: SIAM
Published: 1994-01-01
Total Pages: 414
ISBN-13: 9781611970791
DOWNLOAD EBOOKSpecialists 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.
Abstracts of Technical Reports
Author:
Publisher:
Published: 1992
Total Pages: 52
ISBN-13:
DOWNLOAD EBOOKAdvances in Neural Networks -- ISNN 2010
Author: James Kwok
Publisher: Springer
Published: 2010-05-30
Total Pages: 787
ISBN-13: 3642132782
DOWNLOAD EBOOKThis book and its sister volume collect refereed papers presented at the 7th Inter- tional Symposium on Neural Networks (ISNN 2010), held in Shanghai, China, June 6-9, 2010. Building on the success of the previous six successive ISNN symposiums, ISNN has become a well-established series of popular and high-quality conferences on neural computation and its applications. ISNN aims at providing a platform for scientists, researchers, engineers, as well as students to gather together to present and discuss the latest progresses in neural networks, and applications in diverse areas. Nowadays, the field of neural networks has been fostered far beyond the traditional artificial neural networks. This year, ISNN 2010 received 591 submissions from more than 40 countries and regions. Based on rigorous reviews, 170 papers were selected for publication in the proceedings. The papers collected in the proceedings cover a broad spectrum of fields, ranging from neurophysiological experiments, neural modeling to extensions and applications of neural networks. We have organized the papers into two volumes based on their topics. The first volume, entitled “Advances in Neural Networks- ISNN 2010, Part 1,” covers the following topics: neurophysiological foundation, theory and models, learning and inference, neurodynamics. The second volume en- tled “Advance in Neural Networks ISNN 2010, Part 2” covers the following five topics: SVM and kernel methods, vision and image, data mining and text analysis, BCI and brain imaging, and applications.
Interior Point Algorithms
Author: Yinyu Ye
Publisher: John Wiley & Sons
Published: 2011-10-11
Total Pages: 440
ISBN-13: 1118030958
DOWNLOAD EBOOKThe first comprehensive review of the theory and practice of one oftoday's most powerful optimization techniques. The explosive growth of research into and development of interiorpoint algorithms over the past two decades has significantlyimproved the complexity of linear programming and yielded some oftoday's most sophisticated computing techniques. This book offers acomprehensive and thorough treatment of the theory, analysis, andimplementation of this powerful computational tool. Interior Point Algorithms provides detailed coverage of all basicand advanced aspects of the subject. Beginning with an overview offundamental mathematical procedures, Professor Yinyu Ye movesswiftly on to in-depth explorations of numerous computationalproblems and the algorithms that have been developed to solve them.An indispensable text/reference for students and researchers inapplied mathematics, computer science, operations research,management science, and engineering, Interior Point Algorithms: * Derives various complexity results for linear and convexprogramming * Emphasizes interior point geometry and potential theory * Covers state-of-the-art results for extension, implementation,and other cutting-edge computational techniques * Explores the hottest new research topics, including nonlinearprogramming and nonconvex optimization.
