Methods Of Dynamic And Nonsmooth Optimization

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Methods Of Dynamic And Nonsmooth Optimization

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Author : Frank H. Clarke
language : en
Publisher: SIAM
Release Date : 1989-01-01

Methods Of Dynamic And Nonsmooth Optimization written by Frank H. Clarke and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989-01-01 with Mathematics categories.

Presents the elements of a unified approach to optimization based on "nonsmooth analysis," a term introduced in the 1970's by the author, who is a pioneer in the field. Based on a series of lectures given at a conference at Emory University in 1986, this volume presents its subjects in a self-contained and accessible manner. The topics treated here have been in an active state of development, and this work therefore incorporates more recent results than those presented in 1986. Focuses mainly on deterministic optimal control, the calculus of variations, and mathematical programming. In addition, it features a tutorial in nonsmooth analysis and geometry and demonstrates that the method of value function analysis via proximal normals is a powerful tool in the study of necessary conditions, sufficient conditions, controllability, and sensitivity analysis. The distinction between inductive and deductive methods, the use of Hamiltonians, the verification technique, and penalization are also emphasized.

Methods Of Nonsmooth Optimization In Stochastic Programming

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Author : Wim Stefanus van Ackooij
language : en
Publisher: Springer Nature
Release Date : 2025-05-05

Methods Of Nonsmooth Optimization In Stochastic Programming written by Wim Stefanus van Ackooij and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-05-05 with Business & Economics categories.

This book presents a comprehensive series of methods in nonsmooth optimization, with a particular focus on their application in stochastic programming and dedicated algorithms for decision-making under uncertainty. Each method is accompanied by rigorous mathematical analysis, ensuring a deep understanding of the underlying principles. The theoretical discussions included are essential for comprehending the mechanics of various algorithms and the nature of the solutions they provide—whether they are global, local, stationary, or critical. The book begins by introducing fundamental tools from set-valued analysis, optimization, and probability theory. It then transitions from deterministic to stochastic optimization, starting with a thorough discussion of modeling, understanding uncertainty, and incorporating it into optimization problems. Following this foundation, the book explores numerical algorithms for nonsmooth optimization, covering well-known decomposition techniques and algorithms for convex optimization, mixed-integer convex programming, and nonconvex optimization. Additionally, it introduces numerical algorithms specifically for stochastic programming, focusing on stochastic programming with recourse, chance-constrained optimization, and detailed algorithms for both risk-neutral and risk-averse multistage stochastic programs. The book guides readers through the entire process, from defining optimization models for practical problems to presenting implementable algorithms that can be applied in practice. It is intended for students, practitioners, and scholars who may be unfamiliar with stochastic programming and nonsmooth optimization. The analyses provided are also valuable for practitioners who may not be interested in convergence proofs but wish to understand the nature of the solutions obtained.

Encyclopedia Of Optimization

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Author : Christodoulos A. Floudas
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-09-04

Encyclopedia Of Optimization written by Christodoulos A. Floudas 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 2008-09-04 with Mathematics categories.

The goal of the Encyclopedia of Optimization is to introduce the reader to a complete set of topics that show the spectrum of research, the richness of ideas, and the breadth of applications that has come from this field. The second edition builds on the success of the former edition with more than 150 completely new entries, designed to ensure that the reference addresses recent areas where optimization theories and techniques have advanced. Particularly heavy attention resulted in health science and transportation, with entries such as "Algorithms for Genomics", "Optimization and Radiotherapy Treatment Design", and "Crew Scheduling".

Techniques Of Variational Analysis

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Author : Jonathan M. Borwein
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-06-14

Techniques Of Variational Analysis written by Jonathan M. Borwein 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 2005-06-14 with Mathematics categories.

Borwein is an authority in the area of mathematical optimization, and his book makes an important contribution to variational analysis Provides a good introduction to the topic

The Cahn Hilliard Equation Recent Advances And Applications

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Author : Alain Miranville
language : en
Publisher: SIAM
Release Date : 2019-09-09

The Cahn Hilliard Equation Recent Advances And Applications written by Alain Miranville and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-09-09 with Mathematics categories.

This is the first book to present a detailed discussion of both classical and recent results on the popular Cahn–Hilliard equation and some of its variants. The focus is on mathematical analysis of Cahn–Hilliard models, with an emphasis on thermodynamically relevant logarithmic nonlinear terms, for which several questions are still open. Initially proposed in view of applications to materials science, the Cahn–Hilliard equation is now applied in many other areas, including image processing, biology, ecology, astronomy, and chemistry. In particular, the author addresses applications to image inpainting and tumor growth. Many chapters include open problems and directions for future research. The Cahn-Hilliard Equation: Recent Advances and Applications is intended for graduate students and researchers in applied mathematics, especially those interested in phase separation models and their generalizations and applications to other fields. Materials scientists also will find this text of interest.

Dynamics With Inequalities

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Author : David E. Stewart
language : en
Publisher: SIAM
Release Date : 2011-01-01

Dynamics With Inequalities written by David E. Stewart and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-01-01 with Mathematics categories.

This book addresses dynamics with inequalities comprehensively. The author develops the theory and application of dynamical systems that incorporate some kind of hard inequality constraint, such as mechanical systems with impact; electrical circuits with diodes (as diodes permit current flow in only one direction); and social and economic systems that involve natural or imposed limits (such as traffic flow, which can never be negative, or inventory, which must be stored within a given facility). This book demonstrates that hard limits - eschewed in most dynamical models - are natural models for many dynamic phenomena, and there are ways of creating differential equations with hard constraints that provide accurate models of many physical, biological, and economic systems. The author discusses how finite- and infinite-dimensional problems are treated in a unified way so the theory is applicable to both ordinary differential equations and partial differential equations.

Techniques Of Differential Topology In Relativity

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Author : Roger Penrose
language : en
Publisher: SIAM
Release Date : 1972-01-01

Techniques Of Differential Topology In Relativity written by Roger Penrose and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1972-01-01 with Technology & Engineering categories.

Acquaints the specialist in relativity theory with some global techniques for the treatment of space-times and will provide the pure mathematician with a way into the subject of general relativity.

Lectures On Geometric Methods In Mathematical Physics

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Author : Jerrold E. Marsden
language : en
Publisher: SIAM
Release Date : 1981-01-01

Lectures On Geometric Methods In Mathematical Physics written by Jerrold E. Marsden and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981-01-01 with Science categories.

A monograph on some of the ways geometry and analysis can be used in mathematical problems of physical interest. The roles of symmetry, bifurcation and Hamiltonian systems in diverse applications are explored.

Optimal Control

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Author : Richard Vinter
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-06-25

Optimal Control written by Richard Vinter 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 2010-06-25 with Science categories.

"Each chapter contains a well-written introduction and notes. They include the author's deep insights on the subject matter and provide historical comments and guidance to related literature. This book may well become an important milestone in the literature of optimal control." —Mathematical Reviews "Thanks to a great effort to be self-contained, [this book] renders accessibly the subject to a wide audience. Therefore, it is recommended to all researchers and professionals interested in Optimal Control and its engineering and economic applications. It can serve as an excellent textbook for graduate courses in Optimal Control (with special emphasis on Nonsmooth Analysis)." —Automatica "The book may be an essential resource for potential readers, experts in control and optimization, as well as postgraduates and applied mathematicians, and it will be valued for its accessibility and clear exposition." —Applications of Mathematics

An Introduction To Structured Population Dynamics

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Author : J. M. Cushing
language : en
Publisher: SIAM
Release Date : 1998-01-01

An Introduction To Structured Population Dynamics written by J. M. Cushing and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-01-01 with Science categories.

This monograph introduces the theory of structured population dynamics and its applications, focusing on the asymptotic dynamics of deterministic models.