Mixed-integer conic programming is a generalization of mixed-integer linear programming. In this paper, we present an extension of the duality theory for mixed-integer linear programming (see [M. Güzelsoy and T. K. Ralphs, Int. J. Oper. Res. (Taichung), 4 (2007), pp. 118-137], [G. L. Nemhauser and L. A. Wolsey, Integer and Combinatorial Optimization, Wiley-Interscience, New York, 1988]) to the case of mixed-integer conic programming. In particular, we construct a subadditive dual for mixed-integer conic programming problems. Under a simple condition on the primal problem, we show that strong duality holds.
- Conic programming
- Cutting planes
- Mixed-integer nonlinear programming