Optimization

This book may be regarded as consisting of two parts.

The German edition of this book, first published in 1966, has been quite popular; we did not, however, consider publishing an English edition because a number of excellent textbooks in this field already exist.

This book attempts to present the concepts which underlie the various optimization procedures which are commonly used.

The basis for this book is a number of lectures given frequently by the author to third year students of the Department of Economics at Leningrad State University who specialize in economical cybernetics.

This book is intended as a textbook for a first course in the theory of functions of one complex variable for students who are mathematically mature enough to understand and execute E - 8 arguments.

Our objectives may be briefly stated.

Shortly after the end of World War II high-speed digital computing machines were being developed.

There has been much recent progress in global optimization algo- rithms for nonconvex continuous and discrete problems from both a theoretical and a practical perspective.

Many devices (we say dynamical systems or simply systems) behave like black boxes: they receive an input, this input is transformed following some laws (usually a differential equation) and an output is observed.

In the quest to understand and model the healthy or sick human body, re- searchers and medical doctors are utilizing more and more quantitative tools and techniques.

Changes in the second edition.

As our title reveals, we focus on optimal control methods and applications relevant to linear dynamic economic systems in discrete-time variables.

This monograph is an introduction to optimal control theory for systems governed by vector ordinary differential equations.

Birkhauser Boston, Inc.

The purpose of this four volume series is to make available for college teachers and students samples of important and realistic applications of mathematics which can be covered in undergraduate programs.

As long as a branch of knowledge offers an abundance of problems, it is full of vitality.

Vallombrosa Center was host during the week September 7-12, 1985 to about 40 mathematicians, physical scientists, and engineers, who share a common interest in free surface phenomena.

In 1960, R.

Symmetry methods have long been recognized to be of great importance for the study of the differential equations.

One of the basic tenets of science is that deterministic systems are completely predictable-given the initial condition and the equations describing a system, the behavior of the system can be predicted 1 for all time.

The theory of dynamic games is very rich in nature and very much alive!

This book is a revision of Random Point Processes written by D.

The articles in this volume cover recent work in the area of flow control from the point of view of both engineers and mathematicians.

The common experience in solving control problems shows that optimal control as a function of time proves to be piecewise analytic, having a finite number of jumps (called switches) on any finite-time interval.

Inverse problems and optimal design have come of age as a consequence of the availability of better, more accurate, and more efficient simulation packages.

This IMA Volume in Mathematics and its Applications LARGE-SCALE OPTIMIZATION WITH APPLICATIONS, PART II: OPTIMAL DESIGN AND CONTROL is one of the three volumes based on the proceedings of the 1995 IMA three- week Summer Program on "e;Large-Scale Optimization with Applications to Inverse Problems, Optimal Control and Design, and Molecular and Struc- tural Optimization.

The main subject of this book is perturbation analysis of continuous optimization problems.

This book is based on the papers presented at the International Conference 'Quality Improvement through Statistical Methods' in Cochin, India during December 28-31, 1996.

Are people ever rational?

This self-contained volume surveys three decades of mathematical control theory and at the same time describes how the work of Roger Brockett shaped and influenced its development.

In recent decades, it has become possible to turn the design process into computer algorithms.

A linear optimization problem is the task of minimizing a linear real-valued function of finitely many variables subject to linear con- straints; in general there may be infinitely many constraints.

Although the calculus of variations has ancient origins in questions of Ar- istotle and Zenodoros, its mathematical principles first emerged in the post- calculus investigations of Newton, the Bernoullis, Euler, and Lagrange.

Many important molecular conformation problems, such as protein folding, are expressed as global minimization problems.

This book deals with optimality conditions, algorithms, and discretization tech- niques for nonlinear programming, semi-infinite optimization, and optimal con- trol problems.

This book is concerned with continuous-time Markov chains.

Motivation The latest texts on linear systems for engineering students have begun incorpo- rating chapters on robust control using the state space approach to HOC control for linear finite dimensional time-invariant systems.

Mathematics is playing an ever more important role in the physical and biologi- cal sciences, provoking a blurring of boundaries between scientific disciplines and a resurgence of interest in the modern as well as the classical techniques of applied mathematics.

The goal of this book is to present basic optimization theory and modern computational algorithms in a concise manner.

In wntmg this monograph my aim has been to present a "e;geometric"e; approach to the structural synthesis of multivariable control systems that are linear, time-invariant and of finite dynamic order.

The purpose of this book is to provide core material in nonlinear analysis for mathematicians, physicists, engineers, and mathematical biologists.

This book is the result of our teaching over the years an undergraduate course on Linear Optimal Systems to applied mathematicians and a first-year graduate course on Linear Systems to engineers.

This book collects some recent works on the application of dynamic game and control theory to the analysis of environmental problems.

A theory is the more impressive, the simpler are its premises, the more distinct are the things it connects, and the broader is its range of applicability.