Math 164: General Course Outline
Catalog Description
    164. Optimization. (4) Lecture, three hours; discussion, one hour. Requisite: course 115A. 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.
Textbook
    I. Griva, S. Nash and A. Sofer, Linear and Nonlinear Optimization, 2nd Edition., SIAM.
Reviews & Exams
    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.
Schedule of Lectures

Lecture
Sections
Topics
1
11
Optimization Models
2
2.2
Feasibility and Optimality
3
2.32, 2.4
Convexity; The General Optimization Algorithm
4
3.1
Basic Concepts (of Representation of Linear Constraints)
5
3.1, 4.1
Basic Concepts (of Representation of Linear Constraints); Introduction (to Geometry of Linear Programming)
6
4.2
Standard Form
7-8
4.3
Basic Solutions and Extreme Points
9
4.4
Representation of Solutions; Optimality
10-11
5.2
The Simplex Method
12
6.1
The Dual Problem
13
6.2
Duality Theory
14
6.2.1 and 6.2.2
Complementary Slackness3 and Interpretation of the Dual
15
B4, 2.3.1, 2.6
The Gradient, Hessian and Jacobian; Derivatives and Convexity; Taylor Series4
16
2.7, 2.7.1
Newton's Method for Nonlinear Equations; Systems of Nonlinear Equations
17
10.2
Optimality Conditions (of Unconstrained Optimization)
18
10.3
Newton's Method for Minimization
19
3.2
Null and Range Spaces
20-21
B7, 14.2
Chain Rule; Optimality Conditions for Linear Equality Constraints
22
14.3
The Lagrange Multiplier and the Lagrangian Function
23-24
14.4
Optimality Conditions for Linear Inequality Constraints
25-27
14.5
Optimality Conditions for Nonlinear Constraints
Comments

1Optional
2Cover 2.3.1 later in lecture 15
3This is the linear analog to one of the Karush-Kuhn Tucker conditions in section 14.4.
4All of those sections review material from various lower division math courses.

Outline update: A. Brose and R. Brown, 2/05

NOTE: While this outline includes only one midterm, it is strongly recommended that the instructor considers giving two. It is difficult to schedule a second midterm late in the quarter if it was not announced at the beginning of the course.
For more information, please contact Student Services, ugrad@math.ucla.edu.
 

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