A grand challenge for power grid management lies in how to plan and operate with increasing penetration of distributed energy resources (DERs), such as solar photovoltaics and electric vehicles, which disturb the power grid stability. Existing approaches are unable to verify if a point is on a loadability boundary or characterize all loadability boundary points exactly. This inability leads to ...

The Hadamard maximal determinant (maxdet) problem is to find the maximum determinant H(n) of a square {+1,−1}-matrix of given order n. Such a matrix with maximum determinant is called a Doptimal design of order n. We consider some cases where n 6= 0 mod 4, so the Hadamard bound is not attainable, but bounds due to Barba or Ehlich and Wojtas may be attainable. If R is a matrix with maximal (or c...

This paper deals with the shooting algorithm for optimal control problems with a scalar control and a regular scalar state constraint. Additional conditions are displayed, under which the so-called alternative formulation is equivalent to Pontryagin’s minimum principle. The shooting algorithm appears to be well-posed (invertible Jacobian), iff (i) the no-gap second order sufficient optimality c...

On compact surfaces with or without boundary, Osgood, Phillips and Sarnak proved that the maximum of the determinant of the Laplacian within a conformal class of metrics with fixed area occurs at a metric of constant curvature and, for negative Euler characteristic, exhibited a flow from a given metric to a constant curvature metric along which the determinant increases. The aim of this paper i...

Maximum likelihood estimates of parameters of some spatial models require the computation of the log-determinant of positive-de®nite matrices of the form Iÿ aD, where D is a large, sparse matrix with eigenvalues in ‰ÿ1; 1Š and where 0 < a < 1. With extremely large matrices the usual direct methods of obtaining the log-determinant require too much time and memory. We propose a Monte Carlo estima...