Note Well! This is an previous schedule based on the textbook by Edwin Chong.
| Math4025 Lecture and Homework Schedule, Spring 2004 | Last Modified: January 19, 2004 |
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| Session | Date | Topic | Chapter | Homework Due |
| 1 | 1/20/2004 | Introduction. Examples. Math preliminary: Notation, real vector spaces, linear independence, matrices. | 1,2 | |
| 2 | 1/22 | Math preliminary: Inner product, norm. Eigenvalues and eigenvectors, quadratic forms, calculus of several variables, chain rule, Taylor series, gradient, level sets, directional derivative. | 3,5 | |
| 3 | 1/27 | Definition of optimization problem and types of solutions. Quadratic problems. FONC. | 6 | |
| 4 | 1/29 | SONC. Basic iterative algorithms: form, basic properties, line search. | 6 | |
| 5 | 2/3 | One-dimensional search methods: Golden section search, Newton's method, secant method. | 7 | 1.5, 2.6, 3.2, 3.12a, 5.5, 5.8, 5.9, 6.2, 6.5, 6.11, 6.20 |
| 6 | 2/5 | Multi-dimensional algorithms. Gradient methods: form, steepest descent, convergence. | 8 | |
| 7 | 2/10 | Gradient methods: convergence of fixed step size algorithm, steepest descent algorithm. Order of convergence. | 8 | |
| 8 | 2/12 | Newton's method: form, order of convergence. Properties of general algorithms. | 9 | |
| 9 | 2/17 | Conjugate direction methods: form, properties, conjugate gradient formulas. | 10 | 7.2a,b,d, 8.1, 8.3, 8.13, 8.17, 9.1, 9.3 |
| 10 | 2/19 | Hour Test One: Chapter 1-8 | 11 | |
| 2/24 | Mardis Gras Holiday | |||
| 11 | 2/26 | Newton-Raphson method | 9 | |
| 12 | 3/2 | Newton method: Order & Convexity | 9 & 4 | |
| 13 | 3/4 | Linear Programming | 15 | 9.1-3 |
| 14 | 3/9 | LP Methods | 15 | |
| 15 | 3/11 | Constrained optimization: basic form with equality and inequality constraints. Intro to linear programs, geometric view, standard form. | 15 | |
| 16 | 3/16 | Linear programming: converting to standard form. Linear equations, elementary row operations, basic solutions. | 15,16 | |
| 17 | 3/18 | Basic feasible solutions. Fundamental theorem of LP. Pivoting, changing bases and canonical augmented matrix. | 16 | 15.1, 15.4. 15.5, 15.8 |
| 18 | 3/23 | Moving from one BFS to an adjacent BFS. Reduced cost coefficients. Simplex algorithm. Matrix form of simplex. | 16 | |
| 19 | 3/25 | Artificial problem and feasibility. Two phase algorithm. Duality: form, example. | 16,17 | 16.2, 16.3, 16.9a,c, 16.10 |
| 20 | 3/31 | Weak duality lemma, duality theorem, duality and Simplex algorithm, complementary slackness. Equivalence of feasibility and LP problems. | 17 | 21 | 4/1 | Hour Test Two: Linear Optimization | 17 | 4/6-8 | Spring Break |
| 22 | 4/13 | General equality constraints: basic form, example. Lagrange condition for scalar equality constraint. | 17,19 | |
| 23 | 4/15 | General multivariable Lagrange condition. Tangent and normal space. | 19 | |
| 25 | 4/20 | Minimizing quadratic subject to linear constraint (quadratic programming). Simple linear quadratic regulator problem. Second order conditions. | 19 | 17.3, 17.6, 17.9, 19.6a, 19.10, 19.11a, 19.15a |
| 26 | 4/22 | General equality and inequality constraints: form, example. KKT conditions: inequality and equality constraints. Examples. | 20 | |
| 27 | 4/27 | Project Presentations | ||
| 28 | 4/29 | Project Presentations | ||
| 29 | 5/4 | Non-simplex Algorithms | 18 | |
| 30 | 5/6 | Convex optimization problems. | 21 | |
| 5/12 | Final Examination: 10am - Noon |