Thursday, October 31 2019
12:30pm - 1:45pm
Operations Research Seminar
Gaining or losing perspective

We study mixed-integer nonlinear-optimization formulations of the disjunction $x\in\{0\}\cup[l,u]$, where z is a binary indicator of $x\in[l,u]$, and y ``captures'' x^p, for p>1. This model is useful when activities have operating ranges, we pay a fixed cost for carrying out each activity, and costs on the levels of activities are strictly convex. One well-known concrete application (with p=2) is mean-variance optimization (in the style of Markowitz).

Using volume as a measure to compare convex bodies, we investigate a family of relaxations for this model, employing the inequality $yz^q \geq x^p$, parameterized by the ``lifting exponent'' $q\in [0,p-1]$. These models are higher-dimensional-power-cone representable, and hence tractable. We analytically determine the behavior of these relaxations as functions of l,u,p, and q, enabling use in modeling and algorithmic decisions. We validate our results computationally, for the case of p=2.

This is joint work with J. Lee (Michigan) and D. Skipper (USNA).
Speaker:Emily Speakman
Affiliation:University of Colorado Denver
Location:SCB 4119


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