Math 412 Class log
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(1/20/2016)
Passed out course outline
and emergency information.
What is linear programming? solving
a linear program in 2d, unbounded and infeasible linear programs
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(1/22/2016)
Diet problem, production schedule problem, forms
of a linear problem and converting between forms
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(1/25/2016)
Discussion of different forms of linear problems
and why the form min c^Tx Ax = b
is NOT equivalent to the other forms.
Linear subspaces and affine subspaces,
the two assumptions about LPs in standard form
that we usually make, matrix index notation
basis and bfs solutions
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(1/27/2016)
basic feasible solution introduction,
proposition: basic feasible solution uniquely
determined by a basis,
degenerate basic feasible solution
and degeneracy
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(1/29/2016)
Fundamental theorem of linear programs in
standard form
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(2/1/2016)
The Simplex method
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(2/3/2016)
Unbounded and infeasible linear programs,
the relative cost vector,
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(2/5/2016)
zero level, Cycling, and lexicographic simplex,
intro to lex. simplex
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(2/8/2016)
proof of lex simplex, Bland's rule, 2 phase simplex.
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(2/10/2016)
2 phase simplex continued, Algebraic theorem
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(2/12/2016)
Algebraic Theorem continued, Intro to Duality
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(2/15/2016)
Definition of Dual (Def 3.1), Weak Duality,
The dual of the dual is primal (Theorem 3.2),
Strong duality, Theorem 3.3
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(2/17/2016)
Complementary slackness,
finding a feasible solution is as hard as solving a
linear program
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(2/19/2016)
Farkas Lemma
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(2/22/2016)
Dual simplex method, sensitivity analysis
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(2/24/2016)
matrix games
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(2/26/2016)
matrix games continued
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(2/29/2016)
Integer linear programs,
Graphs, Incidence matrix of a graph,
matching and vertex cover problems,
relaxation of an ILP,
satisfiability
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(3/2/2016)
satisfiability example,
totally unimodular matrices,
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(3/4/2016)
Theorem 13.3, The incidence matrices
of bipartite are TUM
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(3/7/2016)
Directed graphs,
the incidence matrices of directed graphs are TUM,
shortest path problem as an LP,
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(3/9/2016)
shortest path problem as an LP,
the dual of the shortest path problem,
Decomposing flows and circulations
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(3/11/2016)
Intro to the max-flow problem,
revised simplex
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(3/14/2016)
Intro to the max-flow problem,
Revised simplex continued,
max flow with revised simplex.
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(3/16/2016)
max flow with revised simplex cont.
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(3/28/2016)
Intro to Primal-dual
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(3/30/2016)
Primal dual continued
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(4/01/2016)
Dijkstra's algorithm and primal dual
for min-cost path
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(4/06/2016)
Primal dual for min-cost path example,
Primal-dual for max flow intro,
Ford-Fulkerson
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(4/08/2016)
Primal-dual for max-flow continue and
issues with Ford-Fulkerson
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(4/11/2016)
Dual of the max-flow LP and min-cut=max-flow.
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(4/13/2016)
Floyd-Warshall
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(4/18/2016)
Finished Floyd-Warshall,
Intro to min-cost flow and algorithm cycle
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(4/20/2016)
Proved 7.1 using primal-dual method,
Klee-Minty cube and intro to the Ellipsoid method.
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(4/22/2016)
Ellipsoid method
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(4/25/2016)
Ellipsoid method
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(4/27/2016)
Finish Ellipsoid method and start machine scheduling
(4/29/2016)
Machine scheduling
(5/2/2016)
Machine scheduling