On Valid Inequalities for Mixed Integer p-Order Cone Programming

Alexander Vinel () and Pavlo Krokhmal ()
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Alexander Vinel: University of Iowa
Pavlo Krokhmal: University of Iowa

Journal of Optimization Theory and Applications, 2014, vol. 160, issue 2, No 4, 439-456

Abstract: Abstract 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.

Keywords: Valid inequalities; Nonlinear cuts; Mixed integer p-order cone programming; Stochastic optimization; Risk measures (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10957-013-0315-7

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