We study the set $S = \{(x, y) \in \Re_{+} \times Z^{n}: x + B_{j} y_{j} \geq b_{j}, j = 1, \ldots, n\}$, where $B_{j}, b_{j} \in \Re_{+} – \{0\}$, $j = 1, \ldots, n$, and $B_{1} | \cdots | B_{n}$. The set $S$ generalizes the mixed-integer rounding (MIR) set of Nemhauser and Wolsey and … Read more
This paper proposes a filter method for solving nonlinear semidefinite programming problems. Our method extends to this setting the filter SQP (sequential quadratic programming) algorithm, recently introduced for solving nonlinear programming problems, obtaining their respective global convergence results. CitationCMM-B-06/10 – 171 Centre for Mathematical Modelling, UMR 2071, Universidad de Chile-CNRS. Casilla 170-3 Santiago 3, Chile … Read more
Mean-variance portfolios constructed using the sample mean and covariance matrix of asset returns perform poorly out-of-sample due to estimation error. Moreover, it is commonly accepted that estimation error in the sample mean is much larger than in the sample covariance matrix. For this reason, practitioners and researchers have recently focused on the minimum-variance portfolio, which … Read more
We give a simple proof of the Maximum Principle for smooth hybrid control systems by reducing the hybrid problem to an optimal control problem of Pontryagin type and then by using the classical Pontryagin Maximum Principle. CitationA.V. Dmitruk, A.M. Kaganovich. The Hybrid Maximum Principle is a consequence of Pontryagin Maximum Principle, Systems & Control Letters, … Read more
A method for finding all roots of a system of nonlinear equations is described. Our method makes use of C-GRASP, a recently proposed continuous global optimization heuristic. Given a nonlinear system, we solve a corresponding adaptively modified global optimization problem multiple times, each time using C-GRASP, with areas of repulsion around roots that have already … Read more