Math 482 Class log

(08/24/2015 - 1) Passed out course outline and emergency information, first example of a linear program, drawing a 2-d linear program in the plane, definition of a linear program
(08/26/2015 - 2) Examples of unbounded and infeasible LPs, Examples 2.1 and 2.3 from GM book
(08/28/2015 - 3) Transforming general LP General, Canonical and Standard forms (Section 2.1 of PS book), Two assumptions when working in standard form (Ax = b has at least one solution and A has rank m),
(08/31/2015 - 4) Basis, Basic feasible solutions, prop 2 and Lemma 3
(09/02/2015 - 5) degenerate basic feasible solutions, Proposition 4, Lemma 5 (Theorem 2.1 from book)
(09/04/2015 - 6) Lemma 5 cont., Intro to the simplex method.
(09/09/2015 - 7) Simplex method cont., Prop 7, degenerate bfs and the simplex method
(09/11/2015 - 8) unbounded LPs and the simplex method, intro to simplex method as series of row ops,
(09/14/2015 - 9) Theorem 8 and Theorem 9
(09/16/2015 - 10) Cycling and the simplex method, Bland's rule, lexicographic rule. 2-phase simplex
(09/21/2015 - 11) Intro to duality, weak duality
(09/23/2015 - 12) Strong duality, relationships between infeasible,unbounded primal and infeasible and unbounded dual, Solving LPs by finding a feasible point in an auxiliary LP, Intro to complementary slackness,
(09/25/2015 - 13) Proof of complementary slackness, Example use of complementary slackness
(09/28/2015 - 14) Farkas' Lemma and alternate forms, intro to dual simplex
(09/29/2015 - Test 1)
(09/30/2015 - 15) Dual simplex cont., intro to matrix games example Morra
(10/02/2015 - 16) Matrix games - Morra cont., intro to minimax theorem, proposition for minimax theorem
(10/05/2015 - 17) Proof of minimax, dominance relations and example, passed back test 1
(10/07/2015 - 18) (Section 3.4) Shortest path problems, node/arc incidence matrix, shortest path problem as an LP, dual of shortest path problem
(10/09/2015 - 19) Decomposing flows and circulations theorems and corollary (see handout on website), discussion on basic feasible solutions of shortest path LP correspond to shortest paths in the graph
(10/12/2015 - 20) Shortest path LP example, Revised simplex w/ example (section 4.1),
(10/14/2015 - 21) Revised simplex example, max-flow and revised simplex intro (section 4.3)
(10/16/2015 - 22) max-flow and revised simplex example, max-flow and revised simplex in general
(10/16/2015 - 23) finish max-flow and revised simplex, Intro to Primal-dual method
(10/21/2015 - 24) Primal dual example
(10/26/2015 - 25) Primal dual in general, Theorems 5.1 and Theorem 5.3
(10/28/2015 - 26) Dijkstra's algorithm (section 6.4)
(10/30/2015 - 27) Shortest path as primal dual algorithm (section 5.4)
(11/2/2015 - 28) primal dual for max flow (section 5.6) - Ford-Fulkerson algorithm - problem with the Ford-Fulkerson algorithm
(11/4/2015 - 29) Ford-Fulkerson as primal dual algorithm - dual for max flow LP
(11/6/2015 - 30) Max-flow = min-cut
(11/9/2015 - 30) Floyd-Warshall (Section 6.5)
(11/10/2015) - Test 3
(11/11/2015 - 31) Min-cost flow (section 7.1) - algorithm cycle (section 7.2)
(11/16/2015 - 32) Integer linear programs - TSP and satisfiability (section 13.1)