The optimal statistical median of a convex set of arrays |
| |
Authors: | Stefano Benati Romeo Rizzi |
| |
Institution: | (1) Dipartimento di Sociologia e Ricerca sociale, Università di Trento, Via Verdi 6, 38100 Trento, Italy;(2) Dipartimento di Matematica ed Informatica, Università di Udine, Via delle Scienze 208, 33100 Udine, Italy |
| |
Abstract: | We consider the following problem. A set of vectors is given. We want to find the convex combination such that the statistical median of z is maximum. In the application that we have in mind, are the historical return arrays of asset j and are the portfolio weights. Maximizing the median on a convex set of arrays is a continuous non-differentiable, non-concave
optimization problem and it can be shown that the problem belongs to the APX-hard difficulty class. As a consequence, we are
sure that no polynomial time algorithm can ever solve the model, unless P = NP. We propose an implicit enumeration algorithm,
in which bounds on the objective function are calculated using continuous geometric properties of the median. Computational
results are reported. |
| |
Keywords: | Global optimization Median optimization Statistical median and quantile optimization Robust statistics Branch& bound algorithms |
本文献已被 SpringerLink 等数据库收录! |
|