Math 171B (Mathematical Programming)

Course Topics: Numerical methods for nonlinear optimization
Instructor: Prof. Michael Holst (5739 AP&M, mholst@math.ucsd.edu; Office Hours: MW 1-2pm)
TA: Daniel Robinson (VOLUNTEER; 5748 AP&M, drobinso@math.ucsd.edu; Office Hours: W 12:30pm-2:00pm)
Term: Spring 2005
Lecture: 10:00a-10:50a MWF, HSS 1305; Discussion: TBA
Textbook(s): P.E. Gill and M.H. Wright, NUMERICAL OPTIMIZATION, Available at Soft Reserves.
Main Class Webpage: http://ccom.ucsd.edu/~mholst/teaching/ucsd/171b_s05/index.html
Homework Webpage: http://ccom.ucsd.edu/~mholst/teaching/ucsd/171b_s05/hw/index.html

• Week 1: (Chapter 1)
• Mon 3/28:
• Outline; Motivating 1D examples from calculus; Linear Algebra Review: Vector spaces; linear operators and matrices (rectangular and square); eigenvalues/eigenvectors; various special properties of symmetric matrices.
• Wed 3/30:
• Linear Algebra + Calculus: normed spaces and inner-product spaces; convergent and cauchy sequences in R and Rn; continuity of functions in R and Rn.
• Fri 4/1:
• Advanced Calculus: Convergence rates of sequences in R and Rn; continuity and differentiation in R and Rn; gradient, Jacobian, and Hessian; Taylor's Theorem and the Taylor Remainder Formula.
• HW 1 DUE at 5pm Today: Covers Chapter 1. This HW can be found here.
• Week 2: (Chapter 2)
• Mon 4/4:
• Finding zeros of functions of one variable; Newton's method; Finding zeros of functions of several variables; Newton's method in Rn.
• Wed 4/6:
• Convergence properties of Newton's method in Rn; some examples;
• Fri 4/8:
• General convergence proof for Newton's method in Rn.
• Week 3: (Chapter 2)
• Mon 4/11:
• Making Newton's method more robust: Backtracking and damping.
• Wed 4/13:
• Making Newton's method more efficient: approximate Jacobians, the inexact-Newton method.
• Fri 4/15:
• Backtracking and damping for inexact Newton; review for Midterm 1.
• HW 2 DUE at 5pm Today: Covers Chapter 2. This HW can be found here.
• The MATLAB file newton.m that you need for HW2 can be found here.
• Week 4: (Chapter 3)
• Mon 4/18:
• MIDTERM 1 in Class Today: Covers Chapters 1-2 and Homeworks 1-2.
• Wed 4/20:
• Unconstrained optimization: minimization and optimality conditions in one variable.
• Fri 4/22:
• Minimization and optimality conditions in several variables; model-based methods for functions of several variables.
• Week 5: (Chapter 3)
• Mon 4/25:
• Wed 4/27:
• Convergence of steepest descent and condition numbers.
• Fri 4/29:
• (Local) convergence of Newton's method.
• Week 6: (Chapter 3)
• Mon 5/2:
• Fixing Newton via Hessian modification and linesearch.
• HW 3 DUE at 5pm Today: Covers first half of Chapter 3. This HW can be found here.
• NOTE: The due date written on HW 3 is 4/29; please ignore this and just have it in by 5/2.
• Wed 5/4:
• Review of some matrix theory: spectral decomposition.
• Fri 5/6:
• Line-search methods: intro to backtracking.
• Week 7: (Chapter 3 and first part of Chapter 4)
• Mon 5/9:
• Line-search methods: Goldstein-Armijo via linear model
• Wed 5/11:
• Line-search methods: Modified Newton; spectral decomposition
• Fri 5/13:
• Optimization with equality constraints: Feasible paths, constraints c(x), and constraint jacobian Jc(x).
• HW 4 DUE at 5pm Today: Covers second half of Chapter 3. This HW can be found here.
• Week 8: (Chapter 4)
• Mon 5/16:
• Tangent cone, Null(Jc), constraint qualification, Karush-Kuhn-Tucker (KKT) conditions.
• Wed 5/18:
• The Lagrangian and the method of Lagrange multipliers.
• Fri 5/20:
• Quadratic problems w/ equality constraints; optimality conditions; review for Midterm 2.
• Week 9: (Chapter 4)
• Mon 5/23:
• MIDTERM 2 in Class Today: Covers Chapter 3 and Homeworks 3-4.
• Wed 5/25:
• Linear equality constraints.
• Fri 5/27:
• No Lecture (to be made up in 10th week).
• Week 10: (Chapter 4 and Review)
• Mon 5/30:
• Memorial Day (NO LECTURE).
• Wed 6/1:
• Optimization with inequality constraints.
• HW 5 DUE at 5pm Today: Covers Chapter 4. This HW can be found here.
• The MATLAB file newbat.m that you need for HW5 can be found here.
• Fri 6/3:
• Cummulative Review: Chapters 1-4 and Homeworks 1-5.
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