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Conic Programming (Donald Goldfarb and Garud Iyengar)

For the past couple of years we have been working on conic optimization problems and their applications. Conic programming is a generalization of linear programming that includes second-order cone programming and semidefinite programming as special cases. One aspect of this research explores computationally efficient conic programming models for handling data uncertainty in optimization problems.

An application area of this research of particular interest to us is robust portfolio selection. Another aspect of our research on conic programs is focused on developing efficient branch-and-cut algorithms for solving mixed integer conic programs. Mixed integer conic programs are natural models for a wide variety of optimization problems such as the max-cut, the traveling salesman problem, robust eigenvalue problem, etc. Recently we have also begun exploring barrier/penalty function methods for controlling stochastic networks.