Math 482 Class log
- (1/21/2015)
Passed out course outline
and emergency information,
first example of a linear program,
drawing a 2-d linear program in the plane,
relationship between linear programming
and linear algebra
- (1/23/2015)
- (1/26/2015)
Equational form,
Transforming LP to equational form,
Assumptions (Ax = b has at least one solution
and A has rank m),
Examples of feasible regions,
Discussion of the geometry of
the feasible region
Notation A_B and x_B
- (1/28/2015)
definitions:
bfs, basic variable, nonbasic variable,
degenerate bfs, basis (as a subset of [n]),
Proved two proposition:
(4.2.1) Every basis has at most
corresponding bfs ,
(4.2.2) a feasible solution
is basic if and only if A_K has rank |K|
(K is the set of indices j such that x_j > 0).
- (1/30/2015)
Proved Theorem 4.2.3 (Fundamental Theorem),
introduction to tableaus for the simplex method
- (2/2/2015)
Simplex example
- (2/4/2015)
Simplex method in general,
section 5.6
- (2/6/2015)
Two-phase simplex and intro to cycles,
Quiz 1
- (2/9/2015)
Discussed quiz 1 and basic feasible solutions,
Cycling and lexicographic simplex
- (2/11/2015)
Pivot rules includes Bland's rule,
and cycling in general
- (2/13/2015)
Final points on cycling, introduction
to duality, canonical form
- (2/16/2015)
The duality theorem,
dualization recipe
- (2/18/2015)
Complementary slackness,
Farkas Lemma
- (2/20/2015)
- (2/23/2015)
Quiz 2
- (2/24/2015)
Exam 1
- (2/25/2015)
Dual simplex method
Introduction to matrix games
- (2/27/2015)
No class
- (3/2/2015)
Returned exam 1
Minimax theorem 8.1.3
- (3/4/2015)
Introduction to integer programming,
Hall's theorem,
Hall's Theorem from Konig theorem
maximum matching and
minimum vertex cover as LP
- (3/6/2015)
Incidence matrices of graphs and digraphs
maximum matching and
minimum vertex cover with incidence matrices
TU matrices,
Lemma 8.2.3
- (3/9/2015)
Incidence matrices of bipartite graphs
and digraphs are TU.
Shortest path problem as a linear program
- (3/11/2015)
Revised simplex
- (3/13/2015)
Revised simplex - Quiz 2
- (3/16/2015)
Revised simplex and the max flow problem
- (3/17/2015)
Test 2
- (3/19/2015)
Introduction to Primal Dual Simplex
- (3/21/2015)
No class
- (3/30/2015)
Primal dual review simplex review,
Primal dual and shortest path
- (4/1/2015)
Primal dual and shortest path,
- (4/3/2015)
Primal dual and shortest path algorithm,
Primal dual and max flow
- (4/6/2015)
Primal dual and max flow,
augmenting path and cuts
- (4/8/2015)
Min-cost = max-flow,
Simplex with Dantzig's rule not polynomial,
size of a integer, rational,
rational vector and
rational matrix
- (4/10/2015)
Strongly polynomial algorithm,
Ellipsoids,
Introduction to the Ellipsoid algorithm
Quiz 4
- (4/13/2015)
Ellipsoid method
- (4/16/2015)
Exam 3
- (4/15/2015)
Finish discussion of ellipsoid method,
including using the ellipsoid method
for semidefinite programs.
- (4/17/2015)
No class
- (4/20/2015)
Approximation algorithms and a
vertex cover approximation algorithm
section 3.3 and section 3.4
- (4/22/2015)
Section 8.3 - intro to machine
scheduling
- (4/24/2015)
Section 8.3 - finished discussion
of machine scheduling
- (4/27/2015)
discussion on computational complexity
and the satisfiability problem,
brief intro to codes
- (4/29/2015)
Section 8.4 - Introduction to codes
and the Hamming code - defined A(n,k)
- (5/01/2015)
codes continued
- (5/4/2015)
codes continued
- (5/6/2015)
branch and bound for integer programs