تحسين النتائح
ترتيب حسب
من
الى
الصفحة 1
الصفحة 1
Beyond the Worst-Case Analysis of Algorithms
There are no silver bullets in algorithm design, and no single algorithmic idea is powerful and flexible enough to solve every computational problem. Nor are there silver bullets in algorithm analysis, as the most enlightening method for analyzing an algorithm often depends on the problem and the application. However, typical algorithms courses rely almost entirely on a single analysis framework, that of worst-case analysis, wherein an algorithm is assessed by its worst performance on any input of a given size. The purpose of this book is to popularize several alternatives to worst-case analysis and their most notable algorithmic applications, from clustering to linear programming to neural network training. Forty leading researchers have contributed introductions to different facets of this field, emphasizing the most important models and results, many of which can be taught in lectures to beginning graduate students in theoretical computer science and machine learning.
Mathematical Formulas for Economists
This collection of formulas constitutes a compendium of mathematics for eco nomics and business. It contains the most important formulas, statements and algorithms in this significant subfield of modern mathematics and addresses primarily students of economics or business at universities, colleges and trade schools. But people dealing with practical or applied problems will also find this collection to be an efiicient and easy-to-use work of reference. First the book treats mathematical symbols and constants, sets and state ments, number systems and their arithmetic as well as fundamentals of com binatorics. The chapter on sequences and series is followed by mathematics of finance, the representation of functions of one and several independent vari ables, their differential and integral calculus and by differential and difference equations. In each case special emphasis is placed on applications and models in economics. The chapter on linear algebra deals with matrices, vectors, determinants and systems of linear equations. This is followed by the representation of struc tures and algorithms of linear programming. Finally, the reader finds formu las on descriptive statistics (data analysis, ratios, inventory and time series analysis), on probability theory (events, probabilities, random variables and distributions) and on inductive statistics (point and interval estimates, tests). Some important tables complete the work.
Linear Programming and its Applications
This book presents a unified treatment of linear programming. Without sacrificing mathematical rigor, the main emphasis of the book is on models and applications. The most important classes of problems are surveyed and presented by means of mathematical formulations, followed by solution methods and a discussion of a variety of "what-if" scenarios. Non-simplex based solution methods and newer developments such as interior point methods are covered along with a variety of approaches that incorporate multiple objectives in the model.
Complex Scheduling
This book deals with such complex scheduling problems and methods to solve them. It consists of three parts: The ?rst part (Chapters 1 and 2) contains a description of basic scheduling models with applications and an introduction into discrete optimization (covering complexity, shortest path algorithms, linear programming, network ?ow algorithms and general optimization methods). In the second part (Chapter 3) resource-constrained project scheduling problems are considered. Especially, methods like constraint propagation, branch-a- bound algorithms and heuristic procedures are described. Furthermore, lower bounds and general objective functions are discussed.
Linear Programming : Foundations and Extensions
Linear Programming: Foundations and Extensions is an introduction to the field of optimization. The book emphasizes constrained optimization, beginning with a substantial treatment of linear programming, and proceeding to convex analysis, network flows, integer programming, quadratic programming, and convex optimization. The book is carefully written. Specific examples and concrete algorithms precede more abstract topics. Topics are clearly developed with a large number of numerical examples worked out in detail.
Linear Optimization Problems with Inexact Data
Linear programming attracted the interest of mathematicians during and after World War II when the first computers were constructed and methods for solving large linear programming problems were sought in connection with specific practical problems—for example, providing logistical support for the U.S. Armed Forces or modeling national economies. Early attempts to apply linear programming methods to solve practical problems failed to satisfy expectations. There were various reasons for the failure. One of them, which is the central topic of this book, was the inexactness of the data used to create the models. This phenomenon, inherent in most pratical problems, has been dealt with in several ways. At first, linear programming models used "average” values of inherently vague coefficients, but the optimal solutions of these models were not always optimal for the original problem itself. Later researchers developed the stochastic linear programming approach, but this too has its limitations. Recently, interest has been given to linear programming problems with data given as intervals, convex sets and/or fuzzy sets. The individual results of these studies have been promising, but the literature has not presented a unified theory. Linear Optimization Problems with Inexact Data attempts to present a comprehensive treatment of linear optimization with inexact data, summarizing existing results and presenting new ones within a unifying framework.
Linear and Nonlinear Programming
"Linear and Nonlinear Programming" is considered a classic textbook in Optimization. While it is a classic, it also reflects modern theoretical insights. These insights provide structure to what might otherwise be simply a collection of techniques and results, and this is valuable both as a means for learning existing material and for developing new results. One major insight of this type is the connection between the purely analytical character of an optimization problem, expressed perhaps by properties of the necessary conditions, and the behavior of algorithms used to solve a problem. This was a major theme of the first and second editions. Now the third edition has been completely updated with recent Optimization Methods. Yinyu Ye has written chapters and chapter material on a number of these areas including Interior Point Methods.
