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ENCE 724 / BMGT 832  Nonlinear Programming

Approximate Schedule and Homeworks

Class text (BSS):     "Nonlinear Programming Theory and Algorithms," Bazaraa, Sherali, Shetty
Optional text (NS): "Linear and Nonlinear Programming," Nash and Sofer

(Important: Read appropriate parts of chapter, entire chapters not always covered)

Week Date Subject Homeworks
1
Jan 30 Problem Classification, examples
(BSS: Chapter 1; NS: Chapter 1)
HW#1
due Feb 13
2
Feb 6 Definitions of optimality, convexity, optimality conditions for unconstrained problems
(BSS: Chapters 2, 3, 4;NS: Chapter 2, 10)
 
3
Feb 13 Set of feasible directions, tangent cone, inner product cone, Moreau's Decomposition Theorem, Minimum Distance Theorem (BSS: Chapter 5),
GAMS programming language (intro for NLP)
HW#2
due Feb 27
4
Feb 20 Optimality conditions for constrained problems
KKT conditions (geometric + algebraic results)
(BSS: Chapter 4; NS: Chapter 14)
 
5
Feb 27 Project Proposals due at start of class
Motivation for the Karush-Kuhn-Tucker (KKT) conditions (BSS: Chapter 4; NS: Chapter 14)
HW#3
due March 7
6
Mar 6 KKT conditions (geometric + algebraic results)
(BSS: Chapter 4; NS: Chapter 14)
 
7
Mar 13 KKT conditions and generalized convexity, constraint qualifications, second order KKT conditions
(BSS: Chapters 4-5; NS: Chapter 14)
 
8
Mar 20 SPRING BREAK, NO CLASS  
9
Mar 27 In-Class, Exam #1 HW#4
due April 10
10
Apr 3 Duality theory for nonlinear programs
(BSS: Chapter 6; NS: Chapter 14, Section 8)
 
11
Apr 10 -Algorithms for unconstrained optimization (steepest descent, Newton's method, Quasi-Newton methods) (BSS: Chapter 8; NS: Chapter 11), Decomposition

-Algorithms for constrained optimization (book by Conejo et al.)
HW#5
due April 13
12
Apr 17 Decomposition Algorithms for constrained optimization (book by Conejo et al.)  
13
Apr 24 -Feasible Direction Methods for constrained optimization
(BSS: Chapter 10; NS: Chapter 15)

-Penalty Methods for constrained optimization
(BSS: Chapters 9, 10; NS: Chapter 16)
HW#6
due May 8
14
May 1 -Feasible Direction Methods for constrained optimization
(BSS: Chapter 10; NS: Chapter 15)

-Penalty Methods for constrained optimization
(BSS: Chapters 9, 10; NS: Chapter 16)
 
15
May 8 Student Presentations (as indicated) &
Final Reports Due
Date of Final Exam
 
16
  In-Class, Exam #2
(scheduled by the registrar during finals week)
 

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