Download or read book Interior point Polynomial Algorithms in Convex Programming written by Yurii Nesterov and published by SIAM. This book was released on 1994-01-01 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Polynomial Algorithms for Linear Programming written by Michael J. Todd and published by . This book was released on 1986 with total page 54 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Linear Optimization and Extensions written by Manfred Padberg and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 521 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the reviews: "Do you know M.Padberg's Linear Optimization and Extensions? [...] Now here is the continuation of it, discussing the solutions of all its exercises and with detailed analysis of the applications mentioned. Tell your students about it. [...] For those who strive for good exercises and case studies for LP this is an excellent volume." Acta Scientiarum Mathematicarum
Download or read book A Polynomial Algorithm Im Linear Programming written by Arthur Guetter and published by . This book was released on 1981 with total page 40 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Towards randomized strongly polynomial algorithms for linear programming written by Srinivasan Krishnan and published by . This book was released on 1991 with total page 9 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Algorithms written by Sanjoy Dasgupta and published by McGraw-Hill Higher Education. This book was released on 2006 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text, extensively class-tested over a decade at UC Berkeley and UC San Diego, explains the fundamentals of algorithms in a story line that makes the material enjoyable and easy to digest. Emphasis is placed on understanding the crisp mathematical idea behind each algorithm, in a manner that is intuitive and rigorous without being unduly formal. Features include:The use of boxes to strengthen the narrative: pieces that provide historical context, descriptions of how the algorithms are used in practice, and excursions for the mathematically sophisticated. Carefully chosen advanced topics that can be skipped in a standard one-semester course but can be covered in an advanced algorithms course or in a more leisurely two-semester sequence.An accessible treatment of linear programming introduces students to one of the greatest achievements in algorithms. An optional chapter on the quantum algorithm for factoring provides a unique peephole into this exciting topic. In addition to the text DasGupta also offers a Solutions Manual which is available on the Online Learning Center."Algorithms is an outstanding undergraduate text equally informed by the historical roots and contemporary applications of its subject. Like a captivating novel it is a joy to read." Tim Roughgarden Stanford University
Download or read book Understanding and Using Linear Programming written by Jiri Matousek and published by Springer Science & Business Media. This book was released on 2007-07-04 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is an introductory textbook mainly for students of computer science and mathematics. Our guiding phrase is "what every theoretical computer scientist should know about linear programming". A major focus is on applications of linear programming, both in practice and in theory. The book is concise, but at the same time, the main results are covered with complete proofs and in sufficient detail, ready for presentation in class. The book does not require more prerequisites than basic linear algebra, which is summarized in an appendix. One of its main goals is to help the reader to see linear programming "behind the scenes".
Download or read book Progress in Mathematical Programming written by Nimrod Megiddo and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt: The starting point of this volume was a conference entitled "Progress in Mathematical Programming," held at the Asilomar Conference Center in Pacific Grove, California, March 1-4, 1987. The main topic of the conference was developments in the theory and practice of linear programming since Karmarkar's algorithm. There were thirty presentations and approximately fifty people attended. Presentations included new algorithms, new analyses of algorithms, reports on computational experience, and some other topics related to the practice of mathematical programming. Interestingly, most of the progress reported at the conference was on the theoretical side. Several new polynomial algorithms for linear program ming were presented (Barnes-Chopra-Jensen, Goldfarb-Mehrotra, Gonzaga, Kojima-Mizuno-Yoshise, Renegar, Todd, Vaidya, and Ye). Other algorithms presented were by Betke-Gritzmann, Blum, Gill-Murray-Saunders-Wright, Nazareth, Vial, and Zikan-Cottle. Efforts in the theoretical analysis of algo rithms were also reported (Anstreicher, Bayer-Lagarias, Imai, Lagarias, Megiddo-Shub, Lagarias, Smale, and Vanderbei). Computational experiences were reported by Lustig, Tomlin, Todd, Tone, Ye, and Zikan-Cottle. Of special interest, although not in the main direction discussed at the conference, was the report by Rinaldi on the practical solution of some large traveling salesman problems. At the time of the conference, it was still not clear whether the new algorithms developed since Karmarkar's algorithm would replace the simplex method in practice. Alan Hoffman presented results on conditions under which linear programming problems can be solved by greedy algorithms."
Download or read book Theory and Algorithms for Linear Optimization written by Cornelis Roos and published by . This book was released on 1997-03-04 with total page 520 pages. Available in PDF, EPUB and Kindle. Book excerpt: The approach to LO in this book is new in many aspects. In particular the IPM based development of duality theory is surprisingly elegant. The algorithmic parts of the book contain a complete discussion of many algorithmic variants, including predictor-corrector methods, partial updating, higher order methods and sensitivity and parametric analysis.
Download or read book POLYNOMIAL TIME ALGORITHMS FOR written by 朱紫君 and published by Open Dissertation Press. This book was released on 2017-01-27 with total page 84 pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation, "Polynomial Time Algorithms for Linear and Integer Programming" by 朱紫君, Chi-kwan, Chu, was obtained from The University of Hong Kong (Pokfulam, Hong Kong) and is being sold pursuant to Creative Commons: Attribution 3.0 Hong Kong License. The content of this dissertation has not been altered in any way. We have altered the formatting in order to facilitate the ease of printing and reading of the dissertation. All rights not granted by the above license are retained by the author. DOI: 10.5353/th_b3122430 Subjects: Algorithms Polynomials Linear programming Integer programming
Download or read book A New Polynomial Time Algorithm for Linear Programming written by N. Karmarkar and published by . This book was released on 198? with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Algebraic Techniques and Their Use in Describing and Processing Uncertainty written by Hung T. Nguyen and published by Springer Nature. This book was released on 2020-02-13 with total page 170 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses heuristic methods – methods lacking a solid theoretical justification – which are ubiquitous in numerous application areas, and explains techniques that can make heuristic methods more reliable. Focusing on algebraic techniques, i.e., those that use only a few specific features of a situation, it describes various state-of-the-art applications, ranging from fuzzy methods for dealing with imprecision to general optimization methods and quantum-based methods for analyzing economic phenomena. The book also includes recent results from leading researchers, which could (and hopefully will) provide the basis for future applications. As such, it is a valuable resource for mathematicians interested in potential applications of their algebraic results and ideas, as well as for application specialists wanting to discover how algebraic techniques can help in their domains.
Download or read book A Unified Approach to Interior Point Algorithms for Linear Complementarity Problems written by Masakazu Kojima and published by Springer Science & Business Media. This book was released on 1991-09-25 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt: Following Karmarkar's 1984 linear programming algorithm, numerous interior-point algorithms have been proposed for various mathematical programming problems such as linear programming, convex quadratic programming and convex programming in general. This monograph presents a study of interior-point algorithms for the linear complementarity problem (LCP) which is known as a mathematical model for primal-dual pairs of linear programs and convex quadratic programs. A large family of potential reduction algorithms is presented in a unified way for the class of LCPs where the underlying matrix has nonnegative principal minors (P0-matrix). This class includes various important subclasses such as positive semi-definite matrices, P-matrices, P*-matrices introduced in this monograph, and column sufficient matrices. The family contains not only the usual potential reduction algorithms but also path following algorithms and a damped Newton method for the LCP. The main topics are global convergence, global linear convergence, and the polynomial-time convergence of potential reduction algorithms included in the family.
Download or read book Linear Programming written by Howard Karloff and published by Springer Science & Business Media. This book was released on 2008-10-14 with total page 150 pages. Available in PDF, EPUB and Kindle. Book excerpt: To this reviewer’s knowledge, this is the first book accessible to the upper division undergraduate or beginning graduate student that surveys linear programming.... Style is informal. ...Recommended highly for acquisition, since it is not only a textbook, but can also be used for independent reading and study. —Choice Reviews This is a textbook intended for advanced undergraduate or graduate students. It contains both theory and computational practice. —Zentralblatt Math
Download or read book Polynomial time Algorithms for Linear Programming Based Only on Primal Scaling and Projected Gradients of a Potential Function written by Robert Michael Freund and published by . This book was released on 1988 with total page 29 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Very Simple Polynomial time Algorithm for Linear Programming written by Paul Tseng and published by . This book was released on 1988 with total page 11 pages. Available in PDF, EPUB and Kindle. Book excerpt: This document proposes a polynomial-time algorithm for linear programming. This algorithm augments the objective by a logarithmic penalty function and then solves a sequence of quadratic approximations of this program. This algorithms has a complexity of iterations and arithmetic operations, where m is a number of variables and L is the size of the problem encoding in binary. This algorithm does not require knowledge of the optimal value and generates a sequence of primal (Dual) feasible solutions that converges to an optimal primal (dual) solution (the latter property provides a particularly simple stopping criterion). Moreover, this algorithm is simple and intuitive, both in the description and in the analysis - in contrast to existing polynomial-time algorithms. It works exclusively in the original space. Keywords: Karmarkar methods; Quadratic approximation; Logarithmic penalty functions. (KR).
Download or read book Nondifferentiable Optimization and Polynomial Problems written by N.Z. Shor and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 407 pages. Available in PDF, EPUB and Kindle. Book excerpt: Polynomial extremal problems (PEP) constitute one of the most important subclasses of nonlinear programming models. Their distinctive feature is that an objective function and constraints can be expressed by polynomial functions in one or several variables. Let :e = {:e 1, ... , :en} be the vector in n-dimensional real linear space Rn; n PO(:e), PI (:e), ... , Pm (:e) are polynomial functions in R with real coefficients. In general, a PEP can be formulated in the following form: (0.1) find r = inf Po(:e) subject to constraints (0.2) Pi (:e) =0, i=l, ... ,m (a constraint in the form of inequality can be written in the form of equality by introducing a new variable: for example, P( x) ~ 0 is equivalent to P(:e) + y2 = 0). Boolean and mixed polynomial problems can be written in usual form by adding for each boolean variable z the equality: Z2 - Z = O. Let a = {al, ... ,a } be integer vector with nonnegative entries {a;}f=l. n Denote by R[a](:e) monomial in n variables of the form: n R[a](:e) = IT :ef'; ;=1 d(a) = 2:7=1 ai is the total degree of monomial R[a]. Each polynomial in n variables can be written as sum of monomials with nonzero coefficients: P(:e) = L caR[a](:e), aEA{P) IX x Nondifferentiable optimization and polynomial problems where A(P) is the set of monomials contained in polynomial P.
