Professor Alper Atamturk was a speaker at the annual INFORMS conference held this year in Philadelphia from November 1-4. At the conference, Alper delivered his keynote titled “Conic Integer Optimization” (abstract below).
Conic Integer Optimization
In the last 25 years we have experienced significant advances in conic optimization. Polynomial interior point algorithms that have earlier been developed for linear optimization have been extended to second-order cone optimization and semi-definite optimization. The availability of efficient algorithms for convex conic optimization spurred many novel optimization and control applications in diverse areas ranging from medical imaging to statistical learning, from finance to truss design. However, the advances in convex conic optimization and linear integer optimization have until recently not translated into major improvements in conic integer optimization, i.e., conic optimization problems with integer variables. In this talk we will review the recent progress in conic integer optimization. We will discuss cuts, lifting methods, and conic reformulations for improving computations for general as well as special structured problems and connections to submodular optimization for the 0-1 case. We will present applications of conic integer optimization in probabilistic optimization, portfolio optimization, location/inventory optimization with risk pooling.