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Appl Math Optim 2022 13;85(2). Epub 2022 Apr 13.

Dipartimento di Matematica e Applicazioni "R. Caccioppoli", Università di Napoli Federico II, via Cintia, 80126 Napoli, Italy.

A mean-field selective optimal control problem of multipopulation dynamics via transient leadership is considered. The agents in the system are described by their spatial position and their probability of belonging to a certain population. The dynamics in the control problem is characterized by the presence of an activation function which tunes the control on each agent according to the membership to a population, which, in turn, evolves according to a Markov-type jump process. Read More

Appl Math Optim 2022 13;85(2):10. Epub 2022 Apr 13.

Institute for Mathematics and Scientific Computing, University of Graz, Heinrichstrasse 36, 8010 Graz, Austria.

An abstract framework guaranteeing the local continuous differentiability of the value function associated with optimal stabilization problems subject to abstract semilinear parabolic equations subject to a norm constraint on the controls is established. It guarantees that the value function satisfies the associated Hamilton-Jacobi-Bellman equation in the classical sense. The applicability of the developed framework is demonstrated for specific semilinear parabolic equations. Read More

Appl Math Optim 2021 16;83(3):1487-1522. Epub 2019 Jul 16.

Department of Mathematics, University of Maryland, College Park, MD 20742 USA.

We investigate the long-time behavior of solutions to a stochastically forced one-dimensional Navier-Stokes system, describing the motion of a compressible viscous fluid, in the case of linear pressure law. We prove existence of an invariant measure for the Markov process generated by strong solutions. We overcome the difficulties of working with non-Feller Markov semigroups on non-complete metric spaces by generalizing the classical Krylov-Bogoliubov method, and by providing suitable polynomial and exponential moment bounds on the solution, together with pathwise estimates. Read More

Appl Math Optim 2021 11;84(2):1971-2035. Epub 2020 Jul 11.

School of Mathematics and Statistics, University of New South Wales, Sydney, NSW 2052 Australia.

Incompressible Navier-Stokes equations on a thin spherical domain along with free boundary conditions under a random forcing are considered. The convergence of the martingale solution of these equations to the martingale solution of the stochastic Navier-Stokes equations on a sphere as the thickness converges to zero is established. Read More

Appl Math Optim 2021 Sep 8:1-21. Epub 2021 Sep 8.

"Gheorghe Mihoc-Caius Iacob" Institute of Mathematical Statistics and Applied Mathematics of the Romanian Academy, Calea 13 Septembrie 13, Bucharest, Romania.

We consider a mathematical model with five compartments relevant to depict the feature of a certain type of epidemic transmission. We aim to identify some system parameters by means of a minimization problem for a functional involving available measurements for observable compartments, which we treat by an optimal control technique with a state constraint imposed by realistic considerations. The proof of the maximum principle is done by passing to the limit in the conditions of optimality for an appropriate approximating problem. Read More

Appl Math Optim 2021 Jul 24:1-50. Epub 2021 Jul 24.

IMAS UBA-CONICET, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Av Cantilo s/n, Ciudad Universitaria (1428), Buenos Aires, Argentina.

We consider an SIR model with vaccination strategy on a sparse configuration model random graph. We show the convergence of the system when the number of nodes grows and characterize the scaling limits. Then, we prove the existence of optimal controls for the limiting equations formulated in the framework of game theory, both in the centralized and decentralized setting. Read More

Appl Math Optim 2020 6;81(3):1021-1054. Epub 2018 Oct 6.

Institute of Statistics and Mathematical Methods in Economics, Vienna University of Technology, Vienna, Austria.

The paper presents new results about convergence of the gradient projection and the conditional gradient methods for abstract minimization problems on strongly convex sets. In particular, linear convergence is proved, although the objective functional does not need to be convex. Such problems arise, in particular, when a recently developed discretization technique is applied to optimal control problems which are affine with respect to the control. Read More

Appl Math Optim 2015;71(3):379-410

Institute of Computer Science, Faculty of Mathematics and Computer Science, Jagiellonian University, ul. Łojasiewicza 6, 30-348 Kraków, Poland.

In this paper the sensitivity of optimal solutions to control problems described by second order evolution subdifferential inclusions under perturbations of state relations and of cost functionals is investigated. First we establish a new existence result for a class of such inclusions. Then, based on the theory of sequential [Formula: see text]-convergence we recall the abstract scheme concerning convergence of minimal values and minimizers. Read More