Approximation And Optimization In The Caribbean Ii
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Approximation Optimization And Mathematical Economics
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Author : Marc Lassonde
language : en
Publisher: Springer Science & Business Media
Release Date : 2001-01-26
Approximation Optimization And Mathematical Economics written by Marc Lassonde and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-01-26 with Business & Economics categories.
The articles in this proceedings volume reflect the current trends in the theory of approximation, optimization and mathematical economics, and include numerous applications. The book will be of interest to researchers and graduate students involved in functional analysis, approximation theory, mathematical programming and optimization, game theory, mathematical finance and economics.
Fixed Point Theory Variational Analysis And Optimization
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Author : Saleh Abdullah R. Al-Mezel
language : en
Publisher: CRC Press
Release Date : 2014-06-03
Fixed Point Theory Variational Analysis And Optimization written by Saleh Abdullah R. Al-Mezel and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-03 with Business & Economics categories.
Fixed Point Theory, Variational Analysis, and Optimization not only covers three vital branches of nonlinear analysis—fixed point theory, variational inequalities, and vector optimization—but also explains the connections between them, enabling the study of a general form of variational inequality problems related to the optimality conditions involving differentiable or directionally differentiable functions. This essential reference supplies both an introduction to the field and a guideline to the literature, progressing from basic concepts to the latest developments. Packed with detailed proofs and bibliographies for further reading, the text: Examines Mann-type iterations for nonlinear mappings on some classes of a metric space Outlines recent research in fixed point theory in modular function spaces Discusses key results on the existence of continuous approximations and selections for set-valued maps with an emphasis on the nonconvex case Contains definitions, properties, and characterizations of convex, quasiconvex, and pseudoconvex functions, and of their strict counterparts Discusses variational inequalities and variational-like inequalities and their applications Gives an introduction to multi-objective optimization and optimality conditions Explores multi-objective combinatorial optimization (MOCO) problems, or integer programs with multiple objectives Fixed Point Theory, Variational Analysis, and Optimization is a beneficial resource for the research and study of nonlinear analysis, optimization theory, variational inequalities, and mathematical economics. It provides fundamental knowledge of directional derivatives and monotonicity required in understanding and solving variational inequality problems.
Approximation And Optimization In The Caribbean Ii
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Author :
language : en
Publisher: Peter Lang Publishing
Release Date : 1995
Approximation And Optimization In The Caribbean Ii written by and has been published by Peter Lang Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Mathematics categories.
The volume contains original articles and survey papers on approximation theory (e.g. approximation by polynomial and rational functions, approximation by operators, orthogonal polynomials, meromorphic functions), optimization (e.g. integer, nonlinear, quadratic, multi-objective, fractional, semi-infinite), control theory (e.g. singular control problems), equations and inequalities (e.g. complexity), mathematical economy (e.g. core theory, infinite horizon economics), and shows the relations among these topics.
Variational Methods In Partially Ordered Spaces
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Author : Alfred Göpfert
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-04-18
Variational Methods In Partially Ordered Spaces written by Alfred Göpfert and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-04-18 with Business & Economics categories.
This book discusses basic tools of partially ordered spaces and applies them to variational methods in Nonlinear Analysis and for optimizing problems. This book is aimed at graduate students and research mathematicians.
Mathematical Programming With Data Perturbations
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Author : Anthony V. Fiacco
language : en
Publisher: CRC Press
Release Date : 2020-09-24
Mathematical Programming With Data Perturbations written by Anthony V. Fiacco and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-09-24 with Mathematics categories.
Presents research contributions and tutorial expositions on current methodologies for sensitivity, stability and approximation analyses of mathematical programming and related problem structures involving parameters. The text features up-to-date findings on important topics, covering such areas as the effect of perturbations on the performance of algorithms, approximation techniques for optimal control problems, and global error bounds for convex inequalities.
Bi Level Strategies In Semi Infinite Programming
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Author : Oliver Stein
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-01
Bi Level Strategies In Semi Infinite Programming written by Oliver Stein and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-01 with Mathematics categories.
Semi-infinite optimization is a vivid field of active research. Recently semi infinite optimization in a general form has attracted a lot of attention, not only because of its surprising structural aspects, but also due to the large number of applications which can be formulated as general semi-infinite programs. The aim of this book is to highlight structural aspects of general semi-infinite programming, to formulate optimality conditions which take this structure into account, and to give a conceptually new solution method. In fact, under certain assumptions general semi-infinite programs can be solved efficiently when their bi-Ievel structure is exploited appropriately. After a brief introduction with some historical background in Chapter 1 we be gin our presentation by a motivation for the appearance of standard and general semi-infinite optimization problems in applications. Chapter 2 lists a number of problems from engineering and economics which give rise to semi-infinite models, including (reverse) Chebyshev approximation, minimax problems, ro bust optimization, design centering, defect minimization problems for operator equations, and disjunctive programming.
Computer Algebra Handbook
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Author : Johannes Grabmeier
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Computer Algebra Handbook written by Johannes Grabmeier and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Computers categories.
Two ideas lie gleaming on the jeweler's velvet. The first is the calculus, the sec ond, the algorithm. The calculus and the rich body of mathematical analysis to which it gave rise made modern science possible; but it has been the algorithm that has made possible the modern world. -David Berlinski, The Advent of the Algorithm First there was the concept of integers, then there were symbols for integers: I, II, III, 1111, fttt (what might be called a sticks and stones representation); I, II, III, IV, V (Roman numerals); 1, 2, 3, 4, 5 (Arabic numerals), etc. Then there were other concepts with symbols for them and algorithms (sometimes) for ma nipulating the new symbols. Then came collections of mathematical knowledge (tables of mathematical computations, theorems of general results). Soon after algorithms came devices that provided assistancefor carryingout computations. Then mathematical knowledge was organized and structured into several related concepts (and symbols): logic, algebra, analysis, topology, algebraic geometry, number theory, combinatorics, etc. This organization and abstraction lead to new algorithms and new fields like universal algebra. But always our symbol systems reflected and influenced our thinking, our concepts, and our algorithms.
Large Scale Inverse Problems And Quantification Of Uncertainty
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Author : Lorenz Biegler
language : en
Publisher: John Wiley & Sons
Release Date : 2011-06-24
Large Scale Inverse Problems And Quantification Of Uncertainty written by Lorenz Biegler and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-06-24 with Mathematics categories.
This book focuses on computational methods for large-scale statistical inverse problems and provides an introduction to statistical Bayesian and frequentist methodologies. Recent research advances for approximation methods are discussed, along with Kalman filtering methods and optimization-based approaches to solving inverse problems. The aim is to cross-fertilize the perspectives of researchers in the areas of data assimilation, statistics, large-scale optimization, applied and computational mathematics, high performance computing, and cutting-edge applications. The solution to large-scale inverse problems critically depends on methods to reduce computational cost. Recent research approaches tackle this challenge in a variety of different ways. Many of the computational frameworks highlighted in this book build upon state-of-the-art methods for simulation of the forward problem, such as, fast Partial Differential Equation (PDE) solvers, reduced-order models and emulators of the forward problem, stochastic spectral approximations, and ensemble-based approximations, as well as exploiting the machinery for large-scale deterministic optimization through adjoint and other sensitivity analysis methods. Key Features: Brings together the perspectives of researchers in areas of inverse problems and data assimilation. Assesses the current state-of-the-art and identify needs and opportunities for future research. Focuses on the computational methods used to analyze and simulate inverse problems. Written by leading experts of inverse problems and uncertainty quantification. Graduate students and researchers working in statistics, mathematics and engineering will benefit from this book.
Tame Geometry With Application In Smooth Analysis
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Author : Yosef Yomdin
language : en
Publisher: Springer
Release Date : 2004-02-07
Tame Geometry With Application In Smooth Analysis written by Yosef Yomdin and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-02-07 with Mathematics categories.
The Morse-Sard theorem is a rather subtle result and the interplay between the high-order analytic structure of the mappings involved and their geometry rarely becomes apparent. The main reason is that the classical Morse-Sard theorem is basically qualitative. This volume gives a proof and also an "explanation" of the quantitative Morse-Sard theorem and related results, beginning with the study of polynomial (or tame) mappings. The quantitative questions, answered by a combination of the methods of real semialgebraic and tame geometry and integral geometry, turn out to be nontrivial and highly productive. The important advantage of this approach is that it allows the separation of the role of high differentiability and that of algebraic geometry in a smooth setting: all the geometrically relevant phenomena appear already for polynomial mappings. The geometric properties obtained are "stable with respect to approximation", and can be imposed on smooth functions via polynomial approximation.
Orthogonal Polynomials On The Unit Circle Spectral Theory
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Author : Barry Simon
language : en
Publisher: American Mathematical Soc.
Release Date : 2005
Orthogonal Polynomials On The Unit Circle Spectral Theory written by Barry Simon and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Mathematics categories.
This two-part book is a comprehensive overview of the theory of probability measures on the unit circle, viewed especially in terms of the orthogonal polynomials defined by those measures. A major theme involves the connections between the Verblunsky coefficients (the coefficients of the recurrence equation for the orthogonal polynomials) and the measures, an analog of the spectral theory of one-dimensional Schrödinger operators. Among the topics discussed along the way are the asymptotics of Toeplitz determinants (Szegö's theorems), limit theorems for the density of the zeros of orthogonal polynomials, matrix representations for multiplication by z (CMV matrices), periodic Verblunsky coefficients from the point of view of meromorphic functions on hyperelliptic surfaces, and connections between the theories of orthogonal polynomials on the unit circle and on the real line.