Gaining or Losing Perspective

Abstract

We study MINLO (mixed-integer nonlinear optimization) formulations of the disjunction, where z is a binary indicator of, and y “captures”, for. 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) 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, parameterized by the “lifting exponent”. These models are higher-dimensional-power-cone representable, and hence tractable in theory. We analytically determine the behavior of these relaxations as functions of l, u, p and q. We validate our results computationally, for the case of. Furthermore, for, we obtain results on asymptotic behavior and on optimal branching-point selection.