ECE 6444 Optimization Theory: Finite and Infinite Dimensional Systems (Advanced Topics in Controls): Fall 2006: 3 credits: CRN 96164
The course will cover functional analysis —the study of linear vector spaces —to impose simple, intuitive interpretations on complex, infinite-dimensional problems. The early lectures will offer an introduction to functional analysis, with applications to optimization. topics addressed include linear space, Hilbert space, least-squares estimation, dual spaces, and linear operators and adjoints. Later lectures will deal explicitly with optimization theory, discussing: (1) Optimization of functionals , (2) Global theory of constrained optimization , (3) Local theory of constrained optimization, (4) Iterative methods of optimization.
Taught by				Dr. Pushkin Kachroo pushkin@vt.edu
Listserv			ece6444_96164@listserv.vt.edu
Grading			Tests/HW: 65%; Final: 30%; Attendance: 5% Guaranteed Grades: A- ( > 90%); B- ( > 80%); C- ( > 70%);
Lecture Room			Whit 349
Lecture Time			09:05AM - 09:55AM (M, W)
Office Hours			Location: 345 Durham; 10:00 A.M. to 12:00 Noon (M,W,F)
Textbook				Optimization by Vector Space Methods David G. Luenberger			Recommended
							Schaum's Outline of Operations Research Optimal Control Theory: An Introduction by Donald E. Kirk
T.A.					Office Hours
Schedule
Dates	Days	Topics				Textbook
Aug 21	M	Introduction and Overview
	W	Linear Programming (Standard Form)				Ch 1(p1.2,1.3,1.4), Ch2(p2.1,2.2,2.5,2.7,2.8), Chapter 3 (p3.1) (Schaum)
	F	Duality				Ch 4 (P4.1) (Schaum)
Aug 28	M	Integer Programming				Ch 6 (Ex. 6.1, Ex. 6.2) (Schaum)
	W	Unconstrained Single-variable Nonlinear Optimization				Ch 10 (page 169, Theorem 10.1, 10.2, 10.3, p10.14, 10.15, 10.17) (Schaum)
	F	Unconstrained Multivariable Nonlinear Optimization				Ch 11 (page 182, 183, Newton Raphson method, Theorem 11.5,11.6) (Schaum)
Sept 4	M	Lagrange Multipliers				Ch11 (p. 11.1, 11.2, 11.13), Ch 12 (page 198,199,200) (Schaum)
	W	Kuhn Tucker Conditions				Ch 12 (p12.1,12.2,12.5,12.10) (Schaum)
	F	Review
Sept 11	M	Finite Dimensional Optimization (Schaum)				Test 1 (Schaum)
	W	Dynamic Programming on Graphs				Chapter 1, Chapter 2, Chapter 3 (Kirk)
	F	Hamilton Jacobi PDE				Chapter 3 (Kirk)
Sept 18	M	Calculus of Variations				Chapter 4 (Kirk)
	W	Euler-Lagrange equation- single variable				Chapter 4 (Kirk)
	F	Euler-Lagrange equation- multiple variables				Chapter 4 (Kirk)
Sept 25	M	Euler-Lagrange equation-higher derivatives				Chapter 4 (Kirk)
	W	Dynamic Programming, Hamilton Jacobi				Test 2 (Kirk)
	F	Euler-Lagrange equation-Some Boundary Conditions				Chapter 4 (Kirk)
Oct 2	M	Euler-Lagrange equation-with Constraints				Chapter 4 (Kirk)
	W	Euler-Lagrange equation-General Boundary Conditions				Chapter 4 (Kirk)
	F	Hamiltonian Dynamics, Pontryagin’s Principle				Chapter 5 (Kirk)
Oct 9	M	Fall Break
	W	Infinite Dimensional Optimization (Kirk)				Test 3 (Kirk)
	F	Numerical Methods for Infinite Dimensional Optimization				Chapter 6 (Kirk)
Oct 16	M	Main Principles				Chapter 1(Luenberger)
	W	Vector (Linear) Spaces				Chapter 2 (Luenberger)
	F	Vector (Linear) Spaces				Chapter 2 (Luenberger)
Oct 23	M	Vector (Linear) Spaces				Chapter 2 (Luenberger)
	W	Normed Linear Spaces				Chapter 2 (Luenberger)
	F	Normed Linear Spaces				Chapter 2 (Luenberger)
Oct 30	M	Hilbert Space				Chapter 3 (Luenberger)
	W	Hilbert Space				Chapter 3 (Luenberger)
	F					Test 4 (Due)
Nov 6	M	Hilbert Space				Chapter 3 (Luenberger)
	W	Least Squares Estimation				Chapter 4 (Luenberger)
	F	Dual Spaces				Chapter 5 (Luenberger)
Nov 13	M	Dual Spaces				Chapter 5 (Luenberger)
	W	Linear Operators and Adjoints				Chapter 6 (Luenberger)
	F	Linear Operators and Adjoints				Chapter 6 (Luenberger)
Nov 20	M	Thanksgiving Break
	W	Thanksgiving Break
	F	Thanksgiving Break
Nov 27	M	Optimization of Functionals				Chapter 7 (Luenberger)		Test 5 (Due)
	W	Global Theory of Constrained Optimization				Chapter 8 (Luenberger)
	F	Local Theory of Constrained Optimization				Chapter 9 (Luenberger)
Dec 4	M	Iterative Methods				Chapter 10 (Luenberger)			Test 6 (Due)
	W					Classes End
	F	10:05 A.M. – 12:05 P.M.				Final Exam (Comprehensive)

Major Measurable Learning Objectives:

Having successfully completed this course, the student will be able to:

• Formulate the mathematical model for finite and infinite dimensional optimization problems.

• Apply the necessary and/or sufficient conditions to solve various optimization problems.