Mixed Integer Nonlinear Optimization (MINLO)

In MINLO problems, objective and/or constraints are nonlinear and a subset of variables are constrained to have integer value. My work in the area focuses on exact, branch-and-bound methods for solving these problems to global optimality. I have worked with convex and nonconvex problems, both quadratic and general nonlinear. A result of these effort is the Couenne software of which I am the main developer and maintainer.

Discrete Multi-objective Optimization

Optimization problems where one seeks to optimize more than one objective independently are called multi-objective optimization problems. I have carried out research on Mixed Integer Linear Bi-objective problems and developed branch-and-bound mechanisms, specifically fathoming rules, to solve these problems exactly, i.e. to obtain the full Pareto set. I have also worked on the problem of storing and retrieving Pareto-optimal solutions from a suitable data structure in an efficient fashion.

Network Optimization

Early research focused on network design problems with applications to telecommunications. Emphasis was on survivability of networks to single faults and on robustness w.r.t. traffic demand variability.