Symmetry-exploiting cuts for a class of mixed-0/1 second-order cone programs

Sarah Drewes, Sebastian Pokutta
2014 Discrete Optimization  
We will analyze mixed-0/1 second-order cone programs where the continuous and binary variables are solely coupled via the conic constraints. We devise a cutting-plane framework based on an implicit Sherali-Adams reformulation. The resulting cuts are very effective as symmetric solutions are automatically cut off and each equivalence class of 0/1 solutions is visited at most once. Further, we present computational results showing the effectiveness of our method and briefly sketch an application
more » ... n optimal pooling of securities. Date: April 16, 2014/Draft. 2000 Mathematics Subject Classification. Primary 90C11; Secondary 90C57 90C25. 1 solutions, thus vastly reducing the number of outer approximation iterations. We apply these cuts and the resulting decomposition to solve a pooling problem arising in portfolio optimization in finance. Related work. Cutting-planes for mixed-integer second-order cone programs have been extensively investigated. For example in [7] lift-and-project based cuts for mixed 0/1 conic programming problems have been studied. In [2], Gomory mixed-integer rounding cuts for second-order cone programs have been devised and in [3] lifting for conic mixed-integer programming was investigated. A branch-andcut based method for convex mixed 0/1 programming was outlined in [21] and in [10] lift-and-project based cutting-planes as well as subgradient based outer approximations have been applied to solve mixed-integer second-order cone programs. A lifted linear programming branch-and-bound algorithm for second-order cone programs, where second-order cone constraints are approximated via linear ones, was outlined in [22] . Our approach is different as we consider a special class of mixed 0/1 second-order cone programs whose structure we exploit.
doi:10.1016/j.disopt.2014.04.002 fatcat:tmaguogruzcibn5kbwbj5xyah4