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Sina Masihabadi (si136364neo.tamu.edu) Abstract: We introduce the nstep conic MIR inequalities for the socalled polyhedral secondorder conic (PSOC) mixed integer sets. PSOC sets arise in the polyhedral reformulation of the secondorder conic mixed integer programs. Moreover, they are an equivalent representation for any mixed integer set defined by two linear constraints. The simple conic MIR inequalities of Atamtürk and Narayanan (Math Program 122:120, 2010) and the nstep MIR inequalities of Kianfar and Fathi (Math Program 120:313346, 2009) are special cases of the nstep conic MIR inequalities. We first derive the nstep conic MIR inequality for a PSOC set with n integer variables and prove that all the 1step to nstep conic MIR inequalities are facetdefining for the convex hull of this set. We also provide necessary and sufficient conditions for the polyhedral secondorder conic form of this inequality to be valid. Then we use the aforementioned nstep conic MIR facet to derive the nstep conic MIR inequality for a general PSOC set and provide conditions for it to be facetdefining. These inequalities are generated using functions which we refer to as the nstep conic MIR functions. We further show that the nstep conic MIR inequality for a general PSOC set strictly dominates the nstep MIR inequalities written for the two linear constraints that define the PSOC set. We also prove that the nstep MIR inequality for a linear mixed integer constraint is a special case of the nstep conic MIR inequality. Keywords: nstep conic MIR; nstep MIR; conic mixed integer programming; valid inequality; facet Category 1: Integer Programming ((Mixed) Integer Nonlinear Programming ) Category 2: Integer Programming ((Mixed) Integer Linear Programming ) Category 3: Integer Programming (Cutting Plane Approaches ) Citation: Download: Entry Submitted: 11/22/2011 Modify/Update this entry  
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