Approximation and Complexity in Numerical Optimization
There has been much recent progress in approximation algorithms for nonconvex continuous and discrete problems from both a theoretical and a practical perspective. In discrete (or combinatorial) optimization many approaches have been developed rec...
Complexity and Approximation
N COMPUTER applications we are used to live with approximation. Var I ious notions of approximation appear, in fact, in many circumstances. One notable example is the type of approximation that arises in numer ical analysis or in computational geo...
Approximation and Optimization
This book focuses on the development of approximation-related algorithms and their relevant applications. Individual contributions are written by leading experts and reflect emerging directions and connections in data approximation and optimizatio...
Optimization and Approximation
This book provides a basic, initial resource, introducing science and engineering students to the field of optimization. It covers three main areas: mathematical programming, calculus of variations and optimal control, highlighting the ideas and c...
Low Rank Approximation
Data Approximation by Low-complexity Models details the theory, algorithms, and applications of structured low-rank approximation. Efficient local optimization methods and effective suboptimal convex relaxations for Toeplitz, Hankel, and Sylvester...
Numerical Optimization
Just as in its 1st edition, this book starts with illustrations of the ubiquitous character of optimization, and describes numerical algorithms in a tutorial way. It covers fundamental algorithms as well as more specialized and advanced topics for...
Numerical Optimization
Numerical Optimization presents a comprehensive and up-to-date description of the most effective methods in continuous optimization. There are new chapters on nonlinear interior methods and derivative-free methods for optimization, both of which a...
Numerical Optimization
Numerical Optimization presents a comprehensive and up-to-date description of the most effective methods in continuous optimization. There are new chapters on nonlinear interior methods and derivative-free methods for optimization, both of which a...
Numerical Methods and Optimization
Initial training in pure and applied sciences tends to present problem-solving as the process of elaborating explicit closed-form solutions from basic principles, and then using these solutions in numerical applications. This approach is only appl...
Numerical Methods and Optimization in Finance
This book describes computational finance tools. It covers fundamental numerical analysis and computational techniques, such as option pricing, and gives special attention to simulation and optimization. Many chapters are organized as cas...
Numerical Methods and Optimization in Finance
Computationally-intensive tools play an increasingly important role in financial decisions. Many financial problems-ranging from asset allocation to risk management and from option pricing to model calibration-can be efficiently handled usin...
Numerical Linear Algebra and Optimization
Numerical Linear Algebra and Optimization covers the fundamentals of closely related topics: linear systems (linear equations and least-squares) and linear programming (optimizing a linear function subject to linear constraints). For each problem ...
Optimization Methods in Structural Design
This book offers an introduction to numerical optimization methods in structural design. Employing a readily accessible and compact format, the book presents an overview of optimization methods, and equips readers to properly set up optimization p...
Solutions Manual to accompany An Introduction to Numerical Methods and Analysis
A solutions manual to accompany An Introduction to Numerical Methods and Analysis, Third Edition An Introduction to Numerical Methods and Analysis helps students gain a solid understanding of a wide range of numerical approximation methods for sol...
Computational Contact and Impact Mechanics
This book comprehensively treats the formulation and finite element approximation of contact and impact problems in nonlinear mechanics. Intended for students, researchers and practitioners interested in numerical solid and structural analysis as ...
Modeling and Approximation in Heat Transfer
Engineers face many challenges in systems design and research. Modeling and Approximation in Heat Transfer describes the approach to engineering solutions through simplified modeling of the most important physical features and approximating their ...
Elements of Numerical Mathematical Economics with Excel
Elements of Numerical Mathematical Economics with Excel: Static and Dynamic Optimization shows readers how to apply static and dynamic optimization theory in an easy and practical manner, without requiring the mastery of specific pro...
Approximation Theory and Approximation Practice
This is a textbook on classical polynomial and rational approximation theory for the twenty-first century. Aimed at advanced undergraduates and graduate students across all of applied mathematics, it uses MATLAB to teach the fields most important ...
Strong and Weak Approximation of Semilinear Stochastic Evolution Equations
In this book we analyze the error caused by numerical schemes for the approximation of semilinear stochastic evolution equations (SEEq) in a Hilbert space-valued setting. The numerical schemes considered combine Galerkin finite element methods wit...
Numerical Optimization with Computational Errors
This book studies the approximate solutions of optimization problems in¿the presence of computational errors. A number of results are presented on the¿convergence behavior of algorithms in a Hilbert space; these algorithms are examined taking into...
Introduction to Numerical Methods and Analysis
The new edition of the popular introductory textbook on numerical approximation methods and mathematical analysis, with a unique emphasis on real-world application An Introduction to Numerical Methods and Analysis helps students gain a solid under...
Numerical Analysis and Optimization
Numerical Analysis and Optimization
Foundations of Applied Mathematics, Volume 2
In this second book of what will be a four-volume series, the authors present, in a mathematically rigorous way, the essential foundations of both the theory and practice of algorithms, approximation, and optimization-essential topics in modern ap...
Finite Element Methods for Flow Problems
In recent years there have been significant developments in the development of stable and accurate finite element procedures for the numerical approximation of a wide range of fluid mechanics problems. Taking an engineering rather than a mathemati...
Approximations for Digital Computers
Numerical analysts and computer operators in all fields will welcome this publication in book form of Cecil Hastings' well-known approximations for digital computers, formerly issued in loose sheets and available only to a limited number of specia...
Selected Applications of Convex Optimization
This book focuses on the applications of convex optimization and highlights several topics, including support vector machines, parameter estimation, norm approximation and regularization, semi-definite programming problems, convex relaxation, and ...
Implementing Models in Quantitative Finance: Methods and Cases
This book puts numerical methods in action for the purpose of solving practical problems in quantitative finance. The first part develops a toolkit in numerical methods for finance (Monte Carlo, PDE, Stochastic Optimization, Copula, Econometrics)....
Spherical Harmonics and Approximations on the Unit Sphere: An Introduction
These notes provide an introduction to the theory of spherical harmonics in an arbitrary dimension as well as an overview of classical and recent results on some aspects of the approximation of functions by spherical polynomials and numerical inte...
Expansions and Asymptotics for Statistics
Asymptotic methods provide important tools for approximating and analysing functions that arise in probability and statistics. Moreover, the conclusions of asymptotic analysis often supplement the conclusions obtained by numerical methods. Providi...
Finite Element Methods for Maxwell's Equations
Since the middle of the last century, computing power has increased sufficiently that the direct numerical approximation of Maxwell's equations is now an increasingly important tool in science and engineering. Parallel to the increasing use of num...
Numerical Methods for Unconstrained Optimization and Nonlinear Equations
This book has become the standard for a complete, state-of-the-art description of the methods for unconstrained optimization and systems of nonlinear equations. Originally published in 1983, it provides information needed to understand both the th...
Optimization with PDE Constraints
This book on PDE Constrained Optimization contains contributions on the mathematical analysis and numerical solution of constrained optimal control and optimization problems where a partial differential equation (PDE) or a system of PDEs appears a...
Multiphysics Modeling With Finite Element Methods
Finite element methods for approximating partial differential equations that arise in science and engineering analysis find widespread application. Numerical analysis tools make the solutions of coupled physics, mechanics, chemistry, and even biol...
Normal Approximation by Stein's Method
Since its introduction in 1972, Stein's method has offered a completely novel way of evaluating the quality of normal approximations. Through its characterizing equation approach, it is able to provide approximation error bounds in a wide variety ...
Algorithms for Linear-Quadratic Optimization
This textbook offers theoretical, algorithmic and computational guidelines for solving the most frequently encountered linear-quadratic optimization problems. It provides an overview of recent advances in control and systems theory, numerical line...
Structural Optimization
Structural Optimization is intended to supplement the engineer's box of analysis and design tools making optimization as commonplace as the finite element method in the engineering workplace. It begins with an introduction to structural optimizati...
Ruin Probabilities
The book gives a comprehensive treatment of the classical and modern ruin probability theory. Some of the topics are Lundberg's inequality, the Cramér-Lundberg approximation, exact solutions, other approximations (e.g., for heavy-tailed claim size...
Finite Volume Methods for Hyperbolic Problems
This book, first published in 2002, contains an introduction to hyperbolic partial differential equations and a powerful class of numerical methods for approximating their solution, including both linear problems and nonlinear conservation laws. T...
Nonlinear optimization : a basic course
This book is intended for a first course treating nonlinear optimization problems. It starts with a review of the necessary concepts of calculus and linear algebra, including positive definite matrices. The classical numerical optimization methods...