By Lê Nguyên Hoang, Not an Ordinary Seminar – GERAD. March 6th, 2013.
In this talk, I will take you through some of the greatest simple ideas of the 20th century. From operations research to topology, from set theory to graph theory, from fractals to infinity, we will explore different regions of the world of mathematics. While this presentation is primarily aimed at non-mathematicians, it should be of great interest to everyone.
Graphs and the 4 Color Theorem (Trek through Math 2/8)
By Lê Nguyên Hoang | Updated:2016-02 | Views: 0
Optimization by Linear Programming
By Lê Nguyên Hoang | Updated:2016-02 | Views: 7920
Operations Research deals with optimizing industrial systems. Those systems can be very complex and their modeling may require the use of hundreds, thousands or even millions of variables. Optimizing over millions of variables may seem impossible, but it can be done if the optimization problem has a linear structure. Learn more on this linear structure and optimization solutions!
Duality in Linear Programming
By Lê Nguyên Hoang | Updated:2016-01 | Prerequisites: Optimization by Linear Programming, Linear Algebra and Higher Dimensions | Views: 22864
Duality in linear programming yields plenty of amazing results that help understand and improve algorithms of resolution. This article shows the construction of the dual and its interpretation, as well as major results. In particular, matching of primal and dual bases will be dealt, before presenting the issue of degeneracy and its dual interpretation.
Primal and Dual Simplex Methods
By Lê Nguyên Hoang | Updated:2016-02 | Prerequisites: Optimization by Linear Programming, Duality in Linear Programming | Views: 27109
The simplex method is one of the major algorithm of the 20th century, as it enables the resolution of linear problems with millions of variables. An intuitive approach is given. But that's not all. We present an important variant called the dual simplex. Finally, we'll explain its main default, that is, when facing degeneracy.
Optimization by Integer Programming
By Lê Nguyên Hoang | Updated:2016-01 | Prerequisites: Optimization by Linear Programming | Views: 8917
Integer programming is arguably the greatest achievement of applied mathematics. Half of the time, it's what's used to solve real-world problems!
Column Generation and Dantzig-Wolfe Decomposition
By Lê Nguyên Hoang | Updated:2016-02 | Prerequisites: Linear Algebra and Higher Dimensions, Optimization by Linear Programming | Views: 14309
Column generation and the Dantzig-Wolfe decomposition are powerful tricks which have revolutionized optimization addressed to industrial problems, and generated millions and millions of dollars. My PhD supervisor effectively took great advantage of these tricks and founded companies with it. This article explains the tricks.