William W. Hager - Böcker

As optimization researchers tackle larger and larger problems, scale interactions play an increasingly important role. One general strategy for dealing with a large or difficult problem is to partition it into smaller ones, which are hopefully much easier to solve, and then work backwards towards the solution of original problem, using a solution from a previous level as a starting guess at the next level. This volume contains 22 chapters highlighting some recent research. The topics of the chapters selected for this volume are focused on the development of new solution methodologies, including general multilevel solution techniques, for tackling difficult, large-scale optimization problems that arise in science and industry. Applications presented in the book include but are not limited to the circuit placement problem in VLSI design, a wireless sensor location problem, optimal dosages in the treatment of cancer by radiation therapy, and facility location.

This book is a collection of papers presented at the Large Scale Optimization Conference held at the Center for Applied Optimization, University of Florida, Gainesville, in February, 1993. Accurate modelling of scientific problems often leads to the formulation of large-scale optimization problems involving thousands of continuous and/or discrete variables. As a consequence of new algorithmic developments and of the increased power of computers, large-scale optimization has seen a dramatic increase in activities in the past decade. Topics include large-scale linear, nonlinear and stochastic programming, network optimization, decomposition methods, methods for optimal control, non-smooth equations, integer programming and software development. In addition, applications are included in location theory, structural mechanics, molecular configuration, transportation, multi-target tracking and database design. The book aims to provide a useful source of information for faculty, students and researchers in mathematical programming and related fields.

This text presents some advances in optimal control, both in theory, algorithms, and applications. Theoretical developments include the analysis of feedback stability for the thermoelastic systems and extensions of the maximum principle. Algorithmic developments include new formulations of the augmented gradient projection method, and sequential quadratic programming methodologies. Application areas include aerospace design, operation of hydro power stations, and chemical engineering. The text should be of interest to: applied mathematicians; control theorists; engineers involved with aerospace design; chemical engineers; and hydraulic engineers.

This book presents some of the most recent advances in optimal control, both in theory, algorithms, and applications. Theoretical developments include the analysis of feedback stability for the thermoelastic systems and extensions of the maximum principle. Algorithmic developments include new formulations of the augmented gradient projection method, and sequential quadratic programming methodologies. Application areas include aerospace design, operation of hydro power stations, and chemical engineering. Audience: Applied mathematicians, control theorists, engineers involved with aerospace design, chemical engineers, hydraulic engineers.

On February 15-17, 1993, a conference on Large Scale Optimization, hosted by the Center for Applied Optimization, was held at the University of Florida. The con­ ference was supported by the National Science Foundation, the U. S. Army Research Office, and the University of Florida, with endorsements from SIAM, MPS, ORSA and IMACS. Forty one invited speakers presented papers on mathematical program­ ming and optimal control topics with an emphasis on algorithm development, real world applications and numerical results. Participants from Canada, Japan, Sweden, The Netherlands, Germany, Belgium, Greece, and Denmark gave the meeting an important international component. At­ tendees also included representatives from IBM, American Airlines, US Air, United Parcel Serice, AT & T Bell Labs, Thinking Machines, Army High Performance Com­ puting Research Center, and Argonne National Laboratory. In addition, the NSF sponsored attendance of thirteen graduate students from universities in the United States and abroad. Accurate modeling of scientific problems often leads to the formulation of large­ scale optimization problems involving thousands of continuous and/or discrete vari­ ables. Large scale optimization has seen a dramatic increase in activities in the past decade. This has been a natural consequence of new algorithmic developments and of the increased power of computers. For example, decomposition ideas proposed by G. Dantzig and P. Wolfe in the 1960's, are now implement able in distributed process­ ing systems, and today many optimization codes have been implemented on parallel machines.

As optimization researchers tackle larger and larger problems, scale interactions play an increasingly important role. One general strategy for dealing with a large or difficult problem is to partition it into smaller ones, which are hopefully much easier to solve, and then work backwards towards the solution of original problem, using a solution from a previous level as a starting guess at the next level. This volume contains 22 chapters highlighting some recent research. The topics of the chapters selected for this volume are focused on the development of new solution methodologies, including general multilevel solution techniques, for tackling difficult, large-scale optimization problems that arise in science and industry. Applications presented in the book include but are not limited to the circuit placement problem in VLSI design, a wireless sensor location problem, optimal dosages in the treatment of cancer by radiation therapy, and facility location.

Applied Numerical Linear Algebra introduces students to numerical issues that arise in linear algebra and its applications. A wide range of techniques are touched on, including direct to iterative methods, orthogonal factorizations, least squares, eigenproblems, and nonlinear equations.Inside Applied Numerical Linear Algebra, readers will find:Clear and detailed explanations on a wide range of topics from condition numbers to the singular value decomposition.Material on nonlinear systems as well as linear systems.Frequent illustrations using discretizations of boundary-value problems or demonstrating other concepts.Exercises with detailed solutions at the end of the book.Supplemental material available at https://bookstore.siam.org/cl87/bonus.This textbook is appropriate for junior and senior undergraduate students and beginning graduate students in the following courses: Advanced Numerical Analysis, Special Topics on Numerical Analysis, Topics on Data Science, Topics on Numerical Optimization, and Topics on Approximation Theory.

Using material from many different sources in a systematic and unified way, this self-contained book provides both rigorous mathematical theory and practical numerical insights while developing a framework for determining the convergence rate of discrete approximations to optimal control problems. Elements of the framework include the reference point, the truncation error, and a stability theory for the linearized first-order optimality conditions.Within this framework, the discretized control problem has a stationary point whose distance to the reference point is bounded in terms of the truncation error. The theory applies to a broad range of discretizations and provides completely new insights into the convergence theory for discrete approximations in optimal control, including the relationship between orthogonal collocation and Runge–Kutta methods.Throughout the book, derivatives associated with the discretized control problem are expressed in terms of a back-propagated costate. In particular, the objective derivative of a bang-bang or singular control problem with respect to a switch point of the control are obtained, which leads to the efficient solution of a class of nonsmooth control problems using a gradient-based optimizer.