ECG 795 Optimization: Theory and Applications
Fall 2009: 3 credits
The course covers optimization theory and methods. The
theory part develops using and teaching functional analysis
�the study of linear vector spaces �to impose simple, intuitive
interpretations on complex, finite and infinite-dimensional problems.
The course starts from simple optimization problems, unconstrained
and constrained, linear and nonlinear, and then proceeds to
optimization when systems are time varying. Optimization software is
also covered.
Prerequisites: Graduate Standing. 3 credits.
Grading |
Tests/HW: 35%; Projects: 30%; Final: 30%; Attendance: 5%
Guaranteed Grades:
A- ( > 90%); B- ( > 80%); C- ( > 70%);
|
Lecture Room |
SEB 1240 |
Lecture Time |
10:00 PM-11:15 PM MW |
Office Hours |
Location: SEB3218 Time: 11:15 A.M. to 01:00 P.M. MW |
Textbook |
Schaum's Outline of Operations Research,2nd Ed
by Richard Bronson and Govindasami Naadimuthu
Mcgraw Hill 1997
Optimal Control Theory: An Introduction
by Donald E. Kirk,
Dover 2004
Optimization by Vector Space Methods
David G. Luenberger,
Wiley 1997
|
Topics |
Introduction and Overview ;
Linear Programming (Standard Form)
Duality ;
Integer Programming
Unconstrained Single-variable Nonlinear Optimization ;
Unconstrained Multivariable Nonlinear Optimization
Lagrange Multipliers ;
Kuhn Tucker Conditions
Finite Dimensional Optimization ;
Dynamic Programming on Graphs
Hamilton Jacobi PDE ;
Calculus of Variations
Euler-Lagrange equation- single variable ;
Euler-Lagrange equation- multiple variables
Euler-Lagrange equation-higher derivatives ;
Dynamic Programming, Hamilton Jacobi
Euler-Lagrange equation-Some Boundary Conditions ;
Euler-Lagrange equation-with Constraints
Euler-Lagrange equation-General Boundary Conditions ;
Hamiltonian Dynamics, Pontryagin's Principle
Infinite Dimensional Optimization ;
Numerical Methods for Infinite Dimensional Optimization
Vector (Linear) Spaces ;
Normed Linear Spaces
Hilbert Space ;
Least Squares Estimation
Dual Spaces ;
Linear Operators and Adjoints
Optimization of Functionals ;
Global Theory of Constrained Optimization
Local Theory of Constrained Optimization ;
Iterative Methods
|
Test Score Distribution |
Test 1:avg. 22.81/30
Test 2:avg. 26.88/30
Test 3:avg. 24.59/30
Test 4:avg. 25.38/30
Test 5:avg. 25.94/30
Test 5:avg. 19.19/25
|
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Course Calendar
|
Date |
Day |
Topics |
Textbook-Sections/Notes |
Aug
24 |
M |
Introduction to Mathematical Programming
|
Sch. Ch1 |
W |
Introduction to Mathematical Programming
|
Sch Ch1; Solved Problems: 1.1-1.4,1.10,1.11
|
Aug
31 |
M |
Linear Programming
|
|
W |
Linear Programming
|
Sch Ch2; Solved Problems: 2.1-2.21
|
Sep
7 |
M |
Labor Day
|
Labor Day |
W |
|
|
Sep
14 |
M |
Duals, Sensitivity Analysis, and Integer Programming
|
Sch 3.1,2,3,8,;4.1,2,3,8,9;
examples 6.1,2,3, ex. 6.1,2 |
W |
Nonlinear Unconstrained Optimization
|
|
Sep
21 |
M |
|
|
W |
Study: Sch:Ch10: Thm10.1,2,3,4,5; Ch11: All Thms, examples;
Steepest Ascent, Newton-Raphson method; 11.1,2,7
|
Ch12, Thm12.1, Lagrange, Newton-Raphson, Kuhn-Tucker, 12.1,2,5
Examples done in class
|
Sep
28 |
M |
|
|
W |
Introduction to Optimal Control>
|
Kirk: Ch1, 2, 3.1-4 |
Oct
5 |
M |
Dynamic Programming
|
Kirk: Ch3.1-3.4 |
W |
Hamilton-Jacobi
|
Kirk: Ch3.11,3.12 |
Oct
12 |
M |
Calculus of Variations: Fundamentals
|
Kirk: Ch4.1 |
W |
Euler-Lagrange
|
Kirk: Ch4.2 |
Oct
19 |
M |
|
Midsemester |
W |
Unconstrained Optimal Control
|
Kirk: Ch5.1 |
Oct
26 |
M |
Pontryagin's Principle, numerical methods
|
Kirk: Ch5.3, Ch6 |
W |
Linear Spaces
|
Luenberger:Ch1,2 |
Nov
2 |
M |
|
|
W |
Vector (Linear) Spaces Examples
|
Luenberger:Ch2 |
Nov
9 |
M |
Linear Varieties
|
|
W |
Convex Sets
|
|
Nov
16 |
M |
Normed and Banach Spaces
|
|
W |
Weirstrass Theorem
|
|
Nov
23 |
M |
Hilbert Space, Projection Theorem
|
Luenberger:Ch3 |
W |
Least Squares, Operators, and Pseudoinverse
|
Luenberger:Ch4, Ch6 |
Nov
30 |
M |
|
Review |
W |
|
Review |
Dec
7 |
M |
|
Exam Week |
W |
|
Exam Week |
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