Tag Archives: Optimization
MIT Glimpse (Episode 4)
I was interviewed in November 2015 by Alex Albanese on MIT Glimpse. We discussed Benford’s law, cake cutting, and online optimization. We also discussed how to pick the right toilet, why pi sucks, and why you should watch plenty of Youtube videos!
Linear Programming (Trek through Math 1/8)
The Secretary/Toilet Problem and Online Optimization
A large chunk of applied mathematics has focused on optimizing something with respect to all relevant data. However, in practice, especially in the online world, the data is not available to us, and, yet, we're still expected to make nearly optimal decisions. This problem is exemplified by the famous secretary problem, where a manager needs to decide to hire candidates right after interviews, even though he has not yet met all the candidates. In this article, we review this classic as well as many very recent developments.
A Mathematical Guide to Selling
How to best sell a good? Should we auction it like in movies? Since the 1960s, economists have addressed this question mathematically and found surprising results. Most notably, in 1981, Nobel prize winner Roger Myerson proved that most auctions you could think of would win you just as much as any basic auction, but that, as well, you could do better using his approach. Since, today, billions of dollars are at play in online auctions, you can imagine how hot a topic it has now become!
The Addictive Mathematics of the 2048 Tile Game
2048 is the Internet sensation of the year. This very addictive game has been downloaded hundred of millions of times. Interestingly, this game raises plenty of intriguing mathematical questions. This article unveils some of them!
Column Generation and Dantzig-Wolfe Decomposition
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.
The New Big Fish Called Mean-Field Game Theory
In recent years, at the interface of game theory, control theory and statistical mechanics, a new baby of applied mathematics was given birth. Now named mean-field game theory, this new model represents a new active field of research with a huge range of applications! This is mathematics in the making!
Santa Routing and Heuristics in Operations Research
Designing routes to visit customers has become one of applied mathematicians' favorite optimization problems, as companies offer millions to solve them! This article discusses the clever technics they have come up with, and use them to help Santa deliver toys to kids all over the world!
Optimization by Integer Programming
Integer programming is arguably the greatest achievement of applied mathematics. Half of the time, it's what's used to solve real-world problems!
A Model of Football Games
Back then, I simulated the outcome of the 2006 World Cup, based on a modelling of football games. This article explains this model and presents its results.
Differential Calculus and the Geometry of Derivatives
Differential calculus is one of the most important concept of mathematics for science and engineering. This article focuses on its fundamental meaning.
Duality in Linear Programming
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
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.
Dual Variable Stabilization
Simplex methods face issues in case of degeneracy. The dual variable stabilization is a very recent state-of-the-art way to deal with degeneracy. An intuitive understanding is given in this article.
Marriage Assignment Problem and Variants
Marriage problems consist in matching boys and girls. They are a very interesting class of problems that include assignment problems, which have a very large range of applications. Additional results have been found for variants which include the introduction of boys and girls' preferences, and cases where people cannot be categorized into two groups.
Optimization by Linear Programming
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!