An Introduction to the Theories and Applications of Mixed-integer Conic Programming
In this talk we present some basic concepts of mixed-integer conic programs, describe some of its applications, and also show an extension of a 'nice property' of mixed-integer linear programs to the case of general mixed-integer conic programs. This extension is motivated by the algorithmic and theoretical implications that this 'nice property' has in the case of mixed-integer linear programs. In the first part of the talk we give a description of mixed-integer linear programming. In particular we present the basic concepts, give examples of its application to solve some relevant real-life problems, and present some of the approaches used to find optimal solutions.
A special focus will be given to the theory of cuttings plane. In particular, we will present the relationship of cutting planes with the subadditive duality theory for mixed-integer linear programs. In the second part of the talk we give a description of mixed-integer conic programming. In particular, we present the basic concepts, give some examples of its application to relevant real-life problems, and comment is some of its differences with the mixed-integer linear case. In the last part of the talk, we present the extension of the subadditive duality theory for mixed-integer linear programs to the case of mixed-integer conics programs. The last part of the talk is based in joint work with Santanu S. Dey (Georgia Tech) and Juan Pablo Vielma (MIT).
Diego Moran is a 4th year Ph.D. student in Operations Research at Georgia Tech, working with Professor Santanu S. Dey. He finished his undergraduate in mathematical engineering from Universidad de Chile, and earned a master in operations management from the same university. His main research interest is Optimization, and more precisely, theory and applications of mixed-integer programming. In 2012, he won the INFORMS Optimization Society Student Paper Prize with the paper "A Strong Dual for Conic Mixed-Integer Programs (SIAM Journal on Optimization. Co-Authored with Santanu S. Dey and Juan Pablo Vielma).