## 2016-09-01

### Linear Programming (2011) by Barbaros Tansel at Bilkent University

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source: Bilkent Online Courses     2014年8月15日
IE513 Linear Programming:
Theory, algorithms, and computational aspects of linear programming. Formulation of problems as linear programs. Development of simplex algorithm, geometry of simplex method, duality theory, and economic interpretations. Sensitivity analysis. Variants of simplex method..

Lecture 1: Brief history of linear programming and introductory example 38:18
Lecture 2: Example continued with solution and general form of linear programming in canonical maximization form 52:32
Lecture 3: General form linear programming and matrix forms, two formulation examples 53:26
Lecture 4: Examples of linear programming formulation 44:30
Lecture 5: Examples of linear programming formulation (cont) 49:21
Lecture 6: Conversions of constraints and variables. Requirements space 50:37
Lecture 7: Fourier-Motzkin elimination to solve linear inequality systems 50:17
Lecture 8: Convex sets and convex functions 48:50
Lecture 9: Convexity, hyperplanes, half-spaces. 49:23
Lecture 10: Convex hulls, extreme points, vertices 46:23
Lecture 11: Subspaces, affine subspaces 48:10
Lecture 12: Extreme points of polyhedra, basic and basic feasible solutions 51:04
Lecture 13: Equivalence of basic feasible solutions, extreme points and vertices 51:27
Lecture 14: Adjacent basic solutions, polyhedra in standard form and basic solutions for standard form. 43:05
Lecture 15: Adjacent basic solutions, degeneracy, existence of extreme points, rays, directions of convex sets. 50:37
Lecture 16: Directions and unbounded LPs, extreme directions, representation theorem 50:08
Lecture 17: Optimality of extreme points and unboundedness, simplex method example 49:14
Lecture 18: Simplex method example in dictionary form, equation form and tabular form 51:25
Lecture 19: Simplex method explained in terms of basis matrices 49:54
Lecture 20: Simplex Method in matrix form 54:52
Lecture 21: Simplex tableau in matrix form, alternative optima, unbounded solution 50:10
Lecture 22: Finding a starting basic feasible solution 49:06
Lecture 23: 2-Phase Method to find an initiating basic feasible solution 40:16
Lecture 24: Degeneracy and resolution of cycling 48:45
Lecture 25: Revised Simplex method 50:29
Lecture 26: Revised simplex and simplex for bounded variables 48:46
Lecture 27: Simplex for bounded variables 48:28
Lecture 28: Simplex for bounded variables and duality 46:29
Lecture 29: Duality (cont'd) 48:11
Lecture 30: Duality theorems  41:04
Lecture 31: Example and economical interpretation 43:30
Lecture 32: Dual simplex method 37:27
Lecture 33: Sensitivity analysis 49:55
Lecture 34: Range analysis and parametric costs 52:41
Lecture 35: Parametric right hand sides and decomposition 50:28
Lecture 36: Decomposition (cont'd) 47:04
Lecture 37: Decomposition (cont'd) 46:50
Lecture 38: Introduction to minimum cost network flow problems 49:29
Lecture 39: Minimum cost network flows (cont'd) 50:00
Lecture 40: Minimum cost network flows (cont'd) 48:37
Lecture 41: Network simplex method for lower and upper bounded minimum cost network flow problems 1:06:38