Dr. Jiwen He Math 6367-12994

Math 6367-12994: Optimization II
11:30AM-1:00PM TuTh, CBB 214, Spring 2014 - Dr. Jiwen He

Final Exam -- April 24-27
(Take-Home Final)

Part II: Calculus of Variations
Mar. 11 - April 24

Assignment II (April 24)
1.[3,4,7,14,18]; 2.[17,19,20,21,22]; 3.[6,7]

Lecture 24 (April 17) Multidimensional Integrals (1.5), Minimal Area Problems, Natural Boundary Conditions

Lecture 23 (April 15) Vector Values Problems (2.9,2.10,3.13), Isoperimetric Problems, Geodesics on a Surface

Lecture 22 (April 10) Integral Constraints: Lagrangian Multipliers (2.12), Integral Functionals Involving Higher Derivatives (2.11)

Lecture 21 (April 8) Transversal Conditions (3.14), Application - Brachistochrone

Lecture 20 (April 3) Application: Geodesics on a Sphere

Lecture 19 (April 1) Variable End Point Problems (1.6): Natural Boundary Conditions, Application - Brachistochrone

Lecture 18 (Mar. 27) Convex Integral Functionals, Geodesics on a Cylinder,

Lecture 17 (Mar. 25) Applications: Geodesics in Rd, Brachistochrone, Minimal Surface of Revolution

Lecture 16 (Mar. 20) Variation of a Functional, A Necessary Condition for an Extremum (1.3), Simplest Varational Problem. Euler's Equation (1.4)

Lecture 15 (Mar. 18) Functionals, Some Simple Variational Problems (1.1), Function Spaces (1.2)

Midterm Exam -- Mar. 6-8
(Take-Home Midterm)

Part I: Optimal Control and Dynamic Programming
Jan. 14 - Mar. 6

Review (Mar. 6)

Part I.4: Deterministic Continuous Time Optimal Control
Feb. 20 - Mar. 4

Lecture 14 (Mar. 4) Extensions of the minimun principle (3.4)

Lecture 13 (Feb. 27) Pontryagin minimun principle (3.3)

Lecture 12 (Feb. 25) Hamilton-Jacobi-Bellman equation (3.2).

Lecture 11 (Feb. 20) Continuous time optimal control (3.1)

Assignment I (Feb. 18 - extended)
1.[4,10, 14, 25, 26]; 2.[3,8,16]

Lecture 10 (Feb. 18) Dynamic Programming Solution of Blackjack Problem (1.4)

Lecture 9 (Feb. 13) Blackjack Problem (1.4)

Part I.3: Problems with Perfect State Information
Feb. 4 - Feb. 11

Lecture 8 (Feb. 11) Inventory control (4.2) & Dynamic portfolio analysis (4.3)

Lecture 7 (Feb. 6) Linear systems and quadratic cost II (4.1)

Lecture 6 (Feb. 4) Linear systems and quadratic cost I (4.1)

Part I.2: Deterministic Systems and the Shortest Path Problem
Jan. 23 - Jan. 30

Lecture 5 (Jan. 30) Some shortest path applications (2.2)

Lecture 4 (Jan. 23) Finite-state systems and shortest paths (2.1)

Part I.1: Dynamic Programming Algorithm
Jan. 14 - Jan. 21

Lecture 3 (Jan. 21) More examples

Lecture 2 (Jan. 16) Dynamic programming algorithm (1.3)

Lecture 1 (Jan. 14) Introduction (1.1) and the basic problem (1.2)