Author: Jonathan M. BorweinPublisher:
ISBN:
Category : Convex programming
Languages : en
Pages : 16
Book Description
On Entropy Maximization Via Convex Programming
Author: Jonathan M. BorweinPublisher:
ISBN:
Category : Convex programming
Languages : en
Pages : 16
Book Description
An Unconstrained Convex Programming Dual Approach to a Class of Linearly-constrained Entropy Maximization Problem with a Quadric Cost and Its Applications to Transportation Planning Problems
Author: S. C. FangPublisher:
ISBN:
Category : Convex programming
Languages : en
Pages : 46
Book Description
Entropy Optimization and Mathematical Programming
Author: Shu-Cherng FangPublisher: Springer Science & Business Media
ISBN: 1461561310
Category : Business & Economics
Languages : en
Pages : 350
Book Description
Entropy optimization is a useful combination of classical engineering theory (entropy) with mathematical optimization. The resulting entropy optimization models have proved their usefulness with successful applications in areas such as image reconstruction, pattern recognition, statistical inference, queuing theory, spectral analysis, statistical mechanics, transportation planning, urban and regional planning, input-output analysis, portfolio investment, information analysis, and linear and nonlinear programming. While entropy optimization has been used in different fields, a good number of applicable solution methods have been loosely constructed without sufficient mathematical treatment. A systematic presentation with proper mathematical treatment of this material is needed by practitioners and researchers alike in all application areas. The purpose of this book is to meet this need. Entropy Optimization and Mathematical Programming offers perspectives that meet the needs of diverse user communities so that the users can apply entropy optimization techniques with complete comfort and ease. With this consideration, the authors focus on the entropy optimization problems in finite dimensional Euclidean space such that only some basic familiarity with optimization is required of the reader.
A Simple Unconstrained Dual Convex Programming Method for the Computation of Discrete Maximum Entropy Distribution
Author: Patrick BrockettConvex Optimization
Author: Stephen P. BoydPublisher: Cambridge University Press
ISBN: 9780521833783
Category : Business & Economics
Languages : en
Pages : 744
Book Description
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.
Algorithms for Convex Optimization
Author: Nisheeth K. VishnoiPublisher: Cambridge University Press
ISBN: 1108633994
Category : Computers
Languages : en
Pages : 314
Book Description
In the last few years, Algorithms for Convex Optimization have revolutionized algorithm design, both for discrete and continuous optimization problems. For problems like maximum flow, maximum matching, and submodular function minimization, the fastest algorithms involve essential methods such as gradient descent, mirror descent, interior point methods, and ellipsoid methods. The goal of this self-contained book is to enable researchers and professionals in computer science, data science, and machine learning to gain an in-depth understanding of these algorithms. The text emphasizes how to derive key algorithms for convex optimization from first principles and how to establish precise running time bounds. This modern text explains the success of these algorithms in problems of discrete optimization, as well as how these methods have significantly pushed the state of the art of convex optimization itself.
Splitting Algorithms, Modern Operator Theory, and Applications
Author: Heinz H. BauschkePublisher: Springer Nature
ISBN: 3030259390
Category : Mathematics
Languages : en
Pages : 489
Book Description
This book brings together research articles and state-of-the-art surveys in broad areas of optimization and numerical analysis with particular emphasis on algorithms. The discussion also focuses on advances in monotone operator theory and other topics from variational analysis and nonsmooth optimization, especially as they pertain to algorithms and concrete, implementable methods. The theory of monotone operators is a central framework for understanding and analyzing splitting algorithms. Topics discussed in the volume were presented at the interdisciplinary workshop titled Splitting Algorithms, Modern Operator Theory, and Applications held in Oaxaca, Mexico in September, 2017. Dedicated to Jonathan M. Borwein, one of the most versatile mathematicians in contemporary history, this compilation brings theory together with applications in novel and insightful ways.
A Simple Unconstrained Dual Convex Programming Method for the Computation of Discrete Maximum Entropy Distributions
Author: Patrick BrockettPublisher:
ISBN:
Category : Decision making
Languages : en
Pages : 11
Book Description
This document formulates the generalized constrained maximum entropy problem often used in a decision making context as an extended dual convex programming problem. The dual problem is then presented. In this dual setting the primal Lagrange multipliers are precisely the dual variables, and are easily calculated directly by virtue of the simple structure of the dual problem. An example involving the selection of best equipment for an oil spill is presented as an illustration. The authors contrast their solution with those given by previous authors. (Author).
Convex Optimization
Author: Source WikipediaPublisher: Booksllc.Net
ISBN: 9781230772219
Category :
Languages : en
Pages : 24
Book Description
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Pages: 22. Chapters: Barrier function, Conic optimization, Danskin's theorem, Duality (optimization), Duality gap, Ellipsoid method, Entropy maximization, Fenchel's duality theorem, Geodesic convexity, Lagrangian relaxation, Linear programming, Perturbation function, Second-order cone programming, Strong duality, Subgradient method, Weak duality, Wolfe duality. Excerpt: Linear programming (LP, or linear optimization) is a mathematical method for determining a way to achieve the best outcome (such as maximum profit or lowest cost) in a given mathematical model for some list of requirements represented as linear relationships. Linear programming is a specific case of mathematical programming (mathematical optimization). More formally, linear programming is a technique for the optimization of a linear objective function, subject to linear equality and linear inequality constraints. Its feasible region is a convex polyhedron, which is a set defined as the intersection of finitely many half spaces, each of which is defined by a linear inequality. Its objective function is a real-valued affine function defined on this polyhedron. A linear programming algorithm finds a point in the polyhedron where this function has the smallest (or largest) value if such a point exists. Linear programs are problems that can be expressed in canonical form: where x represents the vector of variables (to be determined), c and b are vectors of (known) coefficients, A is a (known) matrix of coefficients, and is the matrix transpose. The expression to be maximized or minimized is called the objective function (cx in this case). The inequalities Ax b are the constraints which specify a convex polytope over which the objective function is to be optimized. In this context, two vectors are comparable when they have the same dimensions. If every entry in the first...
Author: Hsiao-Ying Chang