arXiv subjects

Antonio Marigonda

Publications and source records attributed to Antonio Marigonda.

10 recordsLinked to original sources

arXiv2025

Generalized differentiation in Wasserstein space and application to multiagent control problem

Several concepts of generalized differentiation in Wasserstein space have been proposed in order to deal with the intrinsic nonsmoothness arising in the context of optimization problems in Wasserstein spaces. In this paper we introduce a concept of admissible variation encompassing some of the most popular definitions as special cases, and using it to derive a comparison principle for viscosity solutions of an Hamilton Jacobi Bellman equation following from an optimal control of a multiagent systems.

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arXiv2025

Optimal control for multiagent systems with simultaneous aggregation

In this paper, we introduce an optimal control problem for multi-agent systems with non-local cost which favors simultaneous aggregation of particles. This is done introducing a time-dependent notion of multiplicity whose intrinsic dynamical nature differs from more established geometric-like definitions.

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arXiv2021

Solutions to a system of first order H-J equations related to a debt management problem

The paper studies a system of first order Hamilton-Jacobi equations with discontinuous coefficients, arising from a model of deterministic optimal debt management in infinite time horizon, with exponential discount and currency devaluation. The existence of an equilibrium solution is obtained by a suitable concatenation of backward solutions to the system of Hamilton-Jacobi equations. A detailed analysis of the behavior of the solution as the debt-ratio-income $x^*\to +\infty$ is also provided.

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arXiv2020

Attainability property for a probabilistic target in Wasserstein spaces

In this paper we establish an attainability result for the minimum time function of a control problem in the space of probability measures endowed with Wasserstein distance. The dynamics is provided by a suitable controlled continuity equation, where we impose a nonlocal nonholonomic constraint on the driving vector field, which is assumed to be a Borel selection of a given set-valued map. This model can be used to describe at a macroscopic level a so-called \emph{multiagent system} made of several possible interacting agents.

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arXiv2020

Anisotropic tempered diffusion equations

We introduce a functional framework which is specially suited to formulate several classes of anisotropic evolution equations of tempered diffusion type. Under an amenable set of hypothesis involving a very natural potential function, these models can be shown to belong to the entropy solution framework devised by 4, 5, therefore ensuring well-posedness. We connect the properties of this potential with those of the associated cost function, thus providing a link with optimal transport theory and a supply of new examples of relativistic cost functions. Moreover, we characterize the anisotropic spreading properties of these models and we determine the Rankine-Hugoniot conditions that rule the temporal evolution of jump hypersurfaces under the given anisotropic flows.

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arXiv2019

A Debt Management Problem with Currency Devaluation

We consider a model of debt management, where a sovereign state trade some bonds to service the debt with a pool of risk-neutral competitive foreign investors. At each time, the government decides which fraction of the gross domestic product (GDP) must be used to repay the debt, and how much to devaluate its currency. Both these operations have the effect to reduce the actual size of the debt but have a social cost in terms of welfare sustainability. Moreover, at any time the sovereign state can declare bankruptcy by paying a correspondent bankruptcy cost. We show that these optimization problems admits an equilibrium solution, leading to bankruptcy or to a stationary state, depending on the initial conditions.

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arXiv2019

Generalized Dynamic Programming Principle and Sparse Mean-Field Control Problems

In this paper we study optimal control problems in Wasserstein spaces, which are suitable to describe macroscopic dynamics of multi-particle systems. The dynamics is described by a parametrized continuity equation, in which the Eulerian velocity field is affine w.r.t. some variables. Our aim is to minimize a cost functional which includes a control norm, thus enforcing a \emph{control sparsity} constraint. More precisely, we consider a nonlocal restriction on the total amount of control that can be used depending on the overall state of the evolving mass. We treat in details two main cases: an instantaneous constraint on the control applied to the evolving mass and a cumulative constraint, which depends also on the amount of control used in previous times. For both constraints, we prove the existence of optimal trajectories for general cost functions and that the value function is viscosity solution of a suitable Hamilton-Jacobi-Bellmann equation. Finally, we discuss an abstract Dynamic Programming Principle, providing further applications in the Appendix.

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arXiv2016

A Stochastic Model of Optimal Debt Management and Bankruptcy

A problem of optimal debt management is modeled as a noncooperative game between a borrower and a pool of lenders, in infinite time horizon with exponential discount. The yearly income of the borrower is governed by a stochastic process. When the debt-to-income ratio $x(t)$ reaches a given size $x^*$, bankruptcy instantly occurs. The interest rate charged by the risk-neutral lenders is precisely determined in order to compensate for this possible loss of their investment. For a given bankruptcy threshold $x^*$, existence and properties of optimal feedback strategies for the borrower are studied, in a stochastic framework as well as in a limit deterministic setting. The paper also analyzes how the expected total cost to the borrower changes, depending on different values of $x^*$, changes, depending on different values of $x^*$?.

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arXiv2013

Optimality conditions and regularity results for time optimal control problems with differential inclusions

We study the time optimal control problem with a general target $\mathcal S$ for a class of differential inclusions that satisfy mild smoothness and controllability assumptions. In particular, we do not require Petrov's condition at the boundary of $\mathcal S$. Consequently, the minimum time function $T(\cdot)$ fails to be locally Lipschitz---never mind semiconcave---near $\mathcal S$. Instead of such a regularity, we use an exterior sphere condition for the hypograph of $T(\cdot)$ to develop the analysis. In this way, we obtain dual arc inclusions which we apply to show the constancy of the Hamiltonian along optimal trajectories and other optimality conditions in Hamiltonian form. We also prove an upper bound for the Hausdorff measure of the set of all nonlipschitz points of $T(\cdot)$ which implies that the minimum time function is of special bounded variation.

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arXiv2009

On a class of modified Wasserstein distances induced by concave mobility functions defined on bounded intervals

We study a new class of distances between Radon measures similar to those studied in a recent paper of Dolbeault-Nazaret-Savaré [DNS]. These distances (more correctly pseudo-distances because can assume the value $+\infty$) are defined generalizing the dynamical formulation of the Wasserstein distance by means of a concave mobility function. We are mainly interested in the physical interesting case (not considered in [DNS]) of a concave mobility function defined in a bounded interval. We state the basic properties of the space of measures endowed with this pseudo-distance. Finally, we study in detail two cases: the set of measures defined in $R^d$ with finite moments and the set of measures defined in a bounded convex set. In the two cases we give sufficient conditions for the convergence of sequences with respect to the distance and we prove a property of boundedness.

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