{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

varaiya_notes - i Lecture Notes on Optimization Pravin...

Info icon This preview shows pages 1–8. Sign up to view the full content.

View Full Document Right Arrow Icon
i Lecture Notes on Optimization Pravin Varaiya
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
ii
Image of page 2
Contents 1 INTRODUCTION 1 2 OPTIMIZATION OVER AN OPEN SET 7 3 Optimization with equality constraints 15 4 Linear Programming 27 5 Nonlinear Programming 49 6 Discrete-time optimal control 75 7 Continuous-time linear optimal control 83 8 Coninuous-time optimal control 95 9 Dynamic programing 121 iii
Image of page 3

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
iv CONTENTS
Image of page 4
PREFACE to this edition Notes on Optimization was published in 1971 as part of the Van Nostrand Reinhold Notes on Sys- tem Sciences, edited by George L. Turin. Our aim was to publish short, accessible treatments of graduate-level material in inexpensive books (the price of a book in the series was about five dol- lars). The effort was successful for several years. Van Nostrand Reinhold was then purchased by a conglomerate which cancelled Notes on System Sciences because it was not sufficiently profitable. Books have since become expensive. However, the World Wide Web has again made it possible to publish cheaply. Notes on Optimization has been out of print for 20 years. However, several people have been using it as a text or as a reference in a course. They have urged me to re-publish it. The idea of making it freely available over the Web was attractive because it reaffirmed the original aim. The only obstacle was to retype the manuscript in LaTex. I thank Kate Klohe for doing just that. I would appreciate knowing if you find any mistakes in the book, or if you have suggestions for (small) changes that would improve it. Berkeley, California P.P. Varaiya September, 1998 v
Image of page 5

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
vi CONTENTS
Image of page 6
PREFACE These Notes were developed for a ten-week course I have taught for the past three years to first-year graduate students of the University of California at Berkeley. My objective has been to present, in a compact and unified manner, the main concepts and techniques of mathematical programming and optimal control to students having diverse technical backgrounds. A reasonable knowledge of advanced calculus (up to the Implicit Function Theorem), linear algebra (linear independence, basis, matrix inverse), and linear differential equations (transition matrix, adjoint solution) is sufficient for the reader to follow the Notes . The treatment of the topics presented here is deep. Although the coverage is not encyclopedic, an understanding of this material should enable the reader to follow much of the recent technical literature on nonlinear programming, (deterministic) optimal control, and mathematical economics. The examples and exercises given in the text form an integral part of the Notes and most readers will need to attend to them before continuing further. To facilitate the use of these Notes as a textbook, I have incurred the cost of some repetition in order to make almost all chapters self-contained.
Image of page 7

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 8
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern