Professor, Mathematics — Chair, Applied Mathematics (Graduate Group)
Member, Optimization Laboratory — Member, Computer Science (Graduate Group)
News & Events — Research — Publications — Math Software — Teaching — Other — Contact
The survey is up-to-date with the recent developments in our series Equivariant Perturbation in Gomory and Johnson's Infinite Group Problem I, II, III.
My research interests are mathematical optimization (integer programming) and computational discrete mathematics.
... on primal integer programming:
... on mixed-integer nonlinear optimization:
... on game theory and bilevel optimization:
... on enumerative combinatorics and number theory:
... a textbook and research monograph:
A gentle introduction and state-of-the-art reference to Graver bases, effective generating function methods, Gröbner basis methods, and Nullstellensatz and Positivstellensatz relaxations.
... more...
This software counts lattice points in rational polyhedra using state-of-the-art variants of Barvinok's algorithm, computes Ehrhart polynomials, volumes of polytopes and integrals of polynomial functions over polytopes, and computes the highest coefficients of weighted Ehrhart quasi-polynomials.
This software implements state-of-the-art algorithms for the computation of Graver bases, Hilbert bases, extreme rays of cones, toric Gröbner bases, Markov bases, and more.
This software implements an automated extremality test for piecewise linear functions (which are allowed to be discontinuous) and contains an electronic compendium of extreme functions.
CV information can be found here.
University of California, Davis Department of Mathematics One Shields Avenue Davis, CA 95616 USA
Office: MSB 3143 Phone: none Skype: mkoeppe.ucdavis