
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 12pm)
TA: Daniel Robinson
(VOLUNTEER; 5748 AP&M, drobinso@math.ucsd.edu;
Office Hours: W 12:30pm2:00pm)
Term: Spring 2005
Lecture: 10:00a10:50a 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
READING AND HOMEWORK SCHEDULE
 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
innerproduct 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 inexactNewton 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 12 and Homeworks 12.
 Wed 4/20:
 Unconstrained optimization: minimization and optimality
conditions in one variable.
 Fri 4/22:
 Minimization and optimality conditions in several variables;
modelbased 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:
 Linesearch methods: intro to backtracking.
 Week 7: (Chapter 3 and first part of Chapter 4)
 Mon 5/9:
 Linesearch methods: GoldsteinArmijo via linear model
 Wed 5/11:
 Linesearch 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,
KarushKuhnTucker (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 34.
 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 14 and Homeworks 15.
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