On Valid Inequalities for Mixed Integer p-Order Cone Programming
- 243 Downloads
We discuss two families of valid inequalities for linear mixed integer programming problems with cone constraints of arbitrary order, which arise in the context of stochastic optimization with downside risk measures. In particular, we extend the results of Atamtürk and Narayanan (Math. Program., 122:1–20, 2010, Math. Program., 126:351–363, 2011), who developed mixed integer rounding cuts and lifted cuts for mixed integer programming problems with second-order cone constraints. Numerical experiments conducted on randomly generated problems and portfolio optimization problems with historical data demonstrate the effectiveness of the proposed methods.
KeywordsValid inequalities Nonlinear cuts Mixed integer p-order cone programming Stochastic optimization Risk measures
This work was supported in part by AFOSR grant FA9550-12-1-0142 and NSF grant EPS1101284.
- 3.Vinel, A., Krokhmal, P.: On polyhedral approximations for solving p-order conic programming problems. Working paper (2012) Google Scholar
- 4.Drewes, S.: Mixed integer second order cone programming. Ph.D. Thesis, Technische Universität Darmstadt, Germany (2009) Google Scholar
- 9.Belotti, P., Goez, J., Polik, I., Ralphs, T., Terlaky, T.: A conic representation of the convex hull of disjunctive sets and conic cuts for integer second order cone optimization. Working paper (2012) Google Scholar
- 14.Krokhmal, P., Zabarankin, M., Uryasev, S.: Modeling and optimization of risk. Surv. Oper. Res. Manag. Sci. 16, 49–66 (2011) Google Scholar
- 19.Morenko, Y., Vinel, A., Yu, Z., Krokhmal, P.: On p-cone linear discrimination (2012). Submitted for publication Google Scholar