arXiv subjects

P. Fortuny Ayuso

Publications and source records attributed to P. Fortuny Ayuso.

6 recordsLinked to original sources

arXiv2025

The rational rank of the support of generalized power series solutions of differential and $q$-difference equations

Given a differential or $q$-difference equation $P$ of order $n$, we prove that the set of exponents of a generalized power series solution has its rational rank bounded by the rational rank of the support of $P$ plus $n$. We also prove that when the support of the solution has maximum rational rank, it is convergent. Using the Newton polygon technique, we show also that in the maximum rational rank case, an initial segment can always be completed to a true solution. The techniques are the same for the differential and the $q$-difference case.

math.CA↗

arXiv2025

Mid-term bio-economic optimization of multi-species fisheries

In this paper, we analyze the dynamics of a multi-species fisheries system in the presence of harvesting. We solve the problem of finding the optimal harvesting strategy for a mid-term horizon with a fixed final stock of each species, while maximizing the expected present value of total revenues. The problem is formulated as an optimal control problem. For its solution, we combine techniques derived from Pontryagin's Maximum Principle, cyclic coordinate descent and the shooting method. The algorithm we develop can solve problems both with inter-species competition and with predator-prey behaviors. Several numerical examples are presented to illustrate the different possibilities of the method and a study of the dependence of the behavior on some parameters is performed.

math.OC↗

arXiv2025

Optimal control of counter-terrorism tactics

This paper presents an optimal control problem to analyze the efficacy of counter-terrorism tactics. We present an algorithm that efficiently combines the Minimum Principle of Pontryagin, the shooting method and the cyclic descent of coordinates. We also present a result that allows us to know a priori the steady state solutions. Using this technique we are able to choose parameters that reach a specific solution, of which there are two. Numerical examples are presented to illustrate the possibilities of the method. Finally, we study the sufficient conditions for optimality and suggest an improvement on the functional which also guarantees local optimality.

math.OC↗

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↗

arXiv2020

q-Algebraic Equations, their power series solutions, and the asymptotic behavior of their coefficients

We give a systematic study of q-algebraic equations. The questions of existence, uniqueness and regularity of the solutions are solved in the space of grid-based Hahn series. The regularity is understood in terms of asymptotic behavior of coefficients, and is the main focus of this work. The results and algorithms are illustrated by many examples.

math.CA↗

arXiv2017

The Best-or-Worst and the Postdoc problems

We consider two variants of the secretary problem, the\emph{ Best-or-Worst} and the \emph{Postdoc} problems, which are closely related. First, we prove that both variants, in their standard form with binary payoff 1 or 0, share the same optimal stopping rule. We also consider additional cost/perquisites depending on the number of interviewed candidates. In these situations the optimal strategies are very different. Finally, we also focus on the Best-or-Worst variant with different payments depending on whether the selected candidate is the best or the worst.

math.PR↗