arXiv subjects

M. M Ruiz

Publications and source records attributed to M. M Ruiz.

2 recordsLinked to original sources

arXiv2023

Entry and leaving arcs of turnpikes: their exact computation in the calculus of variations

We settle the question of how to compute the entry and leaving arcs for turnpikes in autonomous variational problems, in the one-dimensional case using the phase space of the vector field associated to the Euler equation, and the initial/final and/or the transversality condition. The results hinge on the realization that extremals are the contours of a well-known function and that that the transversality condition is (generically) a curve. An approximation algorithm is presented and an example included for completeness.

math.OC↗

arXiv2018

The Best-or-Worst and the Postdoc problems with random number of candidates

In this paper we consider two variants of the Secretary problem: The Best-or-Worst and the Postdoc problems. We extend previous work by considering that the number of objects is not known and follows either a discrete Uniform distribution $\mathcal{U}[1,n]$ or a Poisson distribution $\mathcal{P}(λ)$. We show that in any case the optimal strategy is a threshold strategy, we provide the optimal cutoff values and the asymptotic probabilities of success. We also put our results in relation with closely related work.

math.PR↗