Title: Mixed Integer Programming - Strength of adding integer variables
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Mixed Integer Programming is the problem of optimizing a multi-variate function over some domain constraints where some variables are required to take integer values. From a complexity-theoretic perspective, problems with fewer integer variables are easier to solve. However, this is not always the case in practice. We will discuss how performance can be improved when adding integer variables in the context of cutting planes and branch and bound. We will compare several frameworks for doing so in both the context of converting lifting integer and continuous variables to more variables. We will conclude with recent work on mixed-integer quadratic programming and mention some computational results.