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Math 164: General Course Outline

Catalog Description

164. Optimization. (4) Lecture, three hours; discussion, one hour. Requisite: course 115A, 131A. Not open for credit to students with credit for Electrical Engineering 136. Fundamentals of optimization. Linear programming: basic solutions, simplex method, duality theory. Unconstrained optimization, Newton's method for minimization. Nonlinear programming, optimality conditions for constrained problems. Additional topics from linear and nonlinear programming. P/NP or letter grading.

Course Information:

The following schedule, with textbook sections and topics, is based on 27 lectures. The remaining classroom meetings are for leeway, reviews, and a midterm exam. These are scheduled by the individual instructor.

General Information. Math 164 provides an introduction to the theory and algorithms concerned with finding extrema (maxima and minima) of functions subject to constraints.

After a review of topics from multivariable calculus such as the gradient, Hessian, Jacobian, Taylor series, and linear algebra, the course offers the students a working knowledge of optimization theory and methods for linear and nonlinear programming, that is, how to find extrema of linear and nonlinear functions subject to various kinds of constraints.

There are ample opportunities for the students to improve their ability to read and write mathematical proofs as well as to solve applied and theoretical problems.

Textbook

E. K.P. Chong and S. Zak, An Introduction to Optimization, 4th Edition, Wiley.

Outline update: W. Yin, 6/15

Schedule of Lectures

Lecture Section Topics

1

1-5

6

Review vector space, transforms geometry, calculus

Optimization models, constraints
Feasible set, feasible directions

2

7

1D search methods

3

8

Gradient methods, steepest descent method
Analysis of gradient methods

4

9

Newton's method
Modified Newton's method
Gauss-Newton method

5

10
11

The Conjugate Direction methods
Quasi-Newton Methods

6

12

Midterm
Solving Linear equations

7

15
16

Intro. to linear programming, polyhedron
Linear programming Simplex method

8

-
17

Continuation
Duality

9

20
21

Nonlinear optimization with equality constraints
Nonlinear optimization with inequality constraints

10

23

TBA

Algorithms for constrained optimization

Catch-up, Review