Given a generic m x n matrix A, the simplicial complex/C(A) is defined to be the collection of simplices representing maximal lattice point free convex bodies of the form {x : A x <~ b}. The main result of this paper is that the topological space associated with/C (A) is homeomorphic with R m-1 . ( ~ 1998 The Mathematical Programming Society, Inc. Published by Elsevier Science B.V.

September 6, 2009. I’m writing in the wake of ISMP 2009 in Chicago, which ended last weekend. All involved in the organization were delighted with how well the meeting ran, and hope that all attendees (over 1200 of them) found it to be a rich and valuable experience, both professionally and personally. There are too many highlights to recount here; suffice to say the event’s success indicates t...

The fifty-eighth Summer Meeting and the thirty-fourth Colloquium of the American Mathematical Society were held at Queen's University and the Royal Military College, Kingston, Ontario, Canada, from August 31 to September S, 19S3 in conjunction with meetings of the Canadian Mathematical Congress, the Mathematical Association of America, the Institute of Mathematical Statistics, and the Economic ...

September 30, 2010. Starting a new chairmanship of the Mathematical Optimization Society is at the same time very motivating and humbling. Very motivating because I believe the Society is in an excellent position: the membership is strong and the importance of our scientific subject is definitely growing in importance, both in industry and academia. The role of the Society, as the main professi...

March 30, 2011. The Mathematical Optimization Society is alive and active, and the best proof of this statement is the number of innovations that have taken place within the Society since I wrote my last column in Optima. Let me review these innovations briefly. The first innovation, especially from the researcher point of view, is the new internet support which has been introduced for our main...

August 1, 2012. While preparing this column and in my periodic and frantic search for material of interest, I stumbled on this most appropriate motto: Optimum is maximum at a minimum – due to the nu-jazz artist Mr Gaus (no, this is not made up). In view of the coming ISMP festivities, this sounded a marvelous quote, at least if properly interpreted. Indeed, it would be completely wrong to sugge...

July 1, 2011. For the few sorry spirits who, misguided by the general state of the world, thought that mathematical optimization was in theoretical decline or too remote from applications in the real world, the SIOPT Conference on Optimization in Darmstadt in May was a real and vivid counterexample. Indeed this very well attended meeting (600+ participants) was a resounding success in terms of ...