Math 484 - Fall 2014 - Class log

(8/25/2014) Section 1.1 - Theorem 1.1.1 (Taylor's Formula), Definition 1.1.3 global minimizer, strict global minimizer, etc., Theorem 1.1.4, Theorem 1.1.5
(8/27/2014) Section 1.2 - Review of n-dimensional space, distance, open balls, open/closed/compact sets, Definition 1.2.2 global minimizer, strict global minimizer, etc., Theorem 1.2.3
(8/29/2014) Section 1.2 continued - quadratic forms, positive definiteness, positive definiteness, etc. Taylor's Formula for functions from R^n to R, Theorems 1.2.5 and 1.2.9, start of Section 1.3
(9/1/2014) Labor day - no class
(9/3/2014) Section 1.3 - Facts about positive semidefinite matrics, tests for positive definiteness and negative definiteness using principal minors, Theorems 1.3.6 and 1.3.7
(9/5/2014) Section 1.4 Definition and examples of coercive functions, Theorem 1.4.4 and example, Section 1.5 - Review of the spectral theorem and Theorem 1.5.1
(9/8/2014) No class
(9/10/2014) No class
(9/12/2014) No class
(9/15/2014) Convex sets - section 2.1
(9/17/2014) Convex functions - section 2.2
(9/19/2014) Convex functions - section 2.2 continued
(9/22/2014) Arithmetic Geometric mean inequality - examples section 2.4
(9/24/2014) Arithmetic Geometric mean inequality - continued section 2.4 Intro to geometric programming section 2.5
(9/26/2014) Unconstrained Geometric programming -Section 2.5
(9/29/2014) Least squares (section 4.1)
(10/1/2014) Least squares (section 4.1)
(10/3/2014) Subspaces and projections
(10/6/2014) finished section 4.2 and started section 4.3
(10/8/2014) Finished minimum norm solutions and start of section 5.1, Theorem 5.1.1, Corollary 5.1.2 and Theorem 5.1.3
(10/10/2014) Theorem 5.1.4, Theorem 5.1.5, Corollary 5.1.6 and Theorem 5.1.7
(10/13/2014) Theorem 5.1.8 and 5.1.9
(10/15/2014) Theorem 5.1.10, enter to convex programming section 5.2
(10/17/2014) Linear programming examples, Perturbation of a convex program, MP(z), Theorem 5.2.6
(10/20/2014) Example of convex program that are discontinuous at 0 and not differentiable at 0, Theorem 5.2.8
(10/22/2014) Theorem 5.2.11 and examples
(10/24/2014) defined the Lagranian, Theorem 5.2.13
(10/27/2014) Theorem 5.2.14 and example Review of section 5.2, Theorem 5.2.16, extended AM-GM inequality
(10/29/2014) Example of geometric programming
(10/31/2014) Discussion of geometric programs and start of proof of 5.3.5
(11/3/2014) Dual convex programs, definitions: MD, solutions of dual programs, feasible and consistent convex programs, Theorem 5.4.6
(11/5/2014) Example of transforming a problem to a constrained, finished theorem 5.3.5
(11/7/2014) Dicussion of duality, LP weak duality and strong duality, example of solving a LP using its dual, example of a solution to a quadratic program
(11/10/2014) Review of duality method, finished quadratic programmin example, example of a convex program with a duality gap, Intro to penalty methods, penalty functions, Absolute value penalty function, Courant-Beltrami penalty function, Lemma 6.1.3, The penalty method (start of section 6.2)
(11/12/2014) Example of penalty function (6.2.2), Example of exact penalty function (6.2.6) Theorem 6.2.3 and Corollary (6.2.4)
(11/14/2014) Section 6.3, Theorem 6.3.1, Lemma 6.3.2 and Lemma 6.3.4, Statement of Theorem 6.3.5
(11/17/2014) Proof of Theorem 6.3.5, Intro to chapter 3, Newton's Method sequence 3.1.1
(11/19/2014) Example of Newton's method, Theorems 3.1.4 and 3.1.5, Definition of steepest descent method and example.
(11/21/2014) Theorem 3.2.3, Theorem 3.2.5, Definition of a descent method, Theorem 3.2.6 and Corollary 3.2.7
(12/1/2014) Section 3.3, Four criteria for a good update rule, Wolfe's Theorem 3.5.1, Making a symmteric matrix positive definition by adding a multiple of the identity matrix
(12/3/2014) Second 3.5, Broyden's Method, Secant condition, outer product
(12/5/2014) No class (for make-up exam)
(12/8/2014) Discussion about midterm 3, Section 3.5 Intro to BFGS method, Theorem 3.5.1
(12/10/2014) Description of the BFGS method and the DFP method for function minimization