Monday, August 4, 2014

The Frank in the Frank-Wolfe Algorithm of Convex Programming is Female

About 2 weeks ago I was contacted by Martin Jaggi and Zaid Harchaoni who were writing an article on the history of the Frank-Wolfe (1956) algorithm for Optima, which is the newsletter of the Mathematical Optimization Society (formerly the Mathematical Programming Society).  The algorithm was proposed in the paper, "An algorithm for quadratic programming," and published in the journal Naval Research Logistics Quarterly.

They provided me with a text by Frank and stated that Any help towards an more accurate & complete description of that interesting history would be very appreciated.

In reading over the text I was so pleased to see my dissertation advisor's name at Brown University, Stella Dafermos,  mentioned and even my name. I was flooded with nostalgia.

I actually implemented the Frank-Wolfe algorithm as part of my dissertation since part of it entailed conducting computational experiments associated with solving traffic network equilibrium problems, both symmetric ones, which could be reformulated as optimization problems, or asymmetric ones, which were formulated and solved as variational inequality problems. The symmetry condition had to do with the user link cost functions which capture congestion.  

And, yes, the Frank in the Frank-Wolfe algorithm is a female, named Marguerite Frank.

I often mention this to my students when I teach Transportation & Logistics or advanced game theory and network and variational inequality courses. Of course, most suspect that the "Frank" in "Frank-Wolfe" must be a male. Marguerite and Wolfe (Philip) wrote this paper during their time at Princeton and Wolfe went on to IBM. Marguerite spent many years as a professor at Rider University in New Jersey. While at Princeton, they interacted with both Al Tucker and Harold Kuhn, who recently passed away, of Kuhn-Tucker conditions renown.

Marguerite and I had mutual interests also associated with the Braess paradox and in the Annals of Operations Research special volume that I edited in 1993, entitled  Advances in Equilibrium Modeling, Analysis and Computation, she contributed one of the 14 papers, co-authored with
Regina Mladineo, "Computer generation of network cost from one link's equilibrium data.:

Marguerite visited me at the University of Massachusetts Amherst and we had a marvelous conversation on what success means and how to define it.

Marguerite Frank was born in 1927, so she is 87 years young.  Martin Jaggi and Zaid Harchaoni brought to my attention a recent video of Marguerite that was made last December at Lake Tahoe and was posted on Youtube in which she reflects on the algorithm and her contributions. Nice that she is finally getting the attention that she deserves. Exciting to see also that convex programming is garnering renewed interest - we have been doing nonlinear programming throughout because of our research on congested networks from transportation to electric power ones to the Internet.

Both Stella Dafermos and Marguerite Frank represent truly inspiring female STEM pioneers.We owe them a tremendous amount. Sadly, Stella passed away in 1990 at age 49.