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We prove Euler-Lagrange and natural boundary necessary optimality conditions for problems of the calculus of variations which are given by a composition of nabla integrals on an arbitrary time scale. As an application, we get optimality…

Optimization and Control · Mathematics 2011-09-27 Agnieszka B. Malinowska , Delfim F. M. Torres

This paper presents an approach for developing the explanation capabilities of rule-based expert systems managing imprecise and uncertain knowledge. The treatment of uncertainty takes place in the framework of possibility theory where the…

Artificial Intelligence · Computer Science 2013-04-08 Henri Farrency , Henri Prade

We prove a necessary optimality condition of Euler-Lagrange type for quantum variational problems involving Hahn's derivatives of higher-order.

Optimization and Control · Mathematics 2011-11-11 Artur M. C. Brito da Cruz , Natalia Martins , Delfim F. M. Torres

Control systems involving unknown parameters appear a natural framework for applications in which the model design has to take into account various uncertainties. In these circumstances the performance criterion can be given in terms of an…

Optimization and Control · Mathematics 2019-01-15 Piernicola Bettiol , Nathalie Khalil

English version of abstract: The dynamic optimization problems treated by the calculus of variations are usually solved with the help of the 2nd order Euler-Lagrange differential equations. These equations are, generally speaking,…

Optimization and Control · Mathematics 2011-09-02 Paulo D. F. Gouveia , Delfim F. M. Torres

The calculus of variations is a field of mathematical analysis born in 1687 with Newton's problem of minimal resistance, which is concerned with the maxima or minima of integral functionals. Finding the solution of such problems leads to…

Classical Analysis and ODEs · Mathematics 2021-07-30 Delfim F. M. Torres

We generalize the fractional variational problem by allowing the possibility that the lower bound in the fractional derivative does not coincide with the lower bound of the integral that is minimized. Also, for the standard case when these…

Functional Analysis · Mathematics 2015-05-27 Teodor M. Atanackovic , Sanja Konjik , Stevan Pilipovic

In this PhD thesis we introduce a generalized fractional calculus of variations. We consider variational problems containing generalized fractional integrals and derivatives, and study them using standard (indirect) and direct methods. In…

Optimization and Control · Mathematics 2014-03-19 Tatiana Odzijewicz

We prove Euler-Lagrange type equations and transversality conditions for generalized infinite horizon problems of the calculus of variations on time scales. Here the Lagrangian depends on the independent variable, an unknown function and…

Optimization and Control · Mathematics 2013-01-31 Monika Dryl , Delfim F. M. Torres

In classic robust optimization, it is assumed that a set of possible parameter realizations, the uncertainty set, is modeled in a previous step and part of the input. As recent work has shown, finding the most suitable uncertainty set is in…

Optimization and Control · Mathematics 2016-10-18 André Chassein , Marc Goerigk

This paper deals with nonlinear mechanics of an elevator brake system subjected to uncertainties. A deterministic model that relates the braking force with uncertain parameters is deduced from mechanical equilibrium conditions. In order to…

Computational Engineering, Finance, and Science · Computer Science 2024-09-30 Piotr Wolszczak , Pawel Lonkwic , Americo Cunha , Grzegorz Litak , Szymon Molski

The set of closed (or holonomic) measures provides a useful setting for studying optimization problems because it contains all curves, while also enjoying good compactness and convexity properties. We study the way to do variational…

Optimization and Control · Mathematics 2018-10-19 Rodolfo Rios-Zertuche

We study more general variational problems on time scales. Previous results are generalized by proving necessary optimality conditions for (i) variational problems involving delta derivatives of more than the first order, and (ii) problems…

Optimization and Control · Mathematics 2007-05-23 Rui A. C. Ferreira , Delfim F. M. Torres

A numerical study of an algorithm proposed by Gusein Guseinov, which determines approximations to the optimal solution of problems of calculus of variations using two discretizations and correspondent Euler-Lagrange equations, is…

Optimization and Control · Mathematics 2010-05-05 Celia T. L. M. Pereira , Pedro A. F. Cruz , Delfim F. M. Torres

One of the main objectives of science is the recognition of a general pattern in a particular phenomenon in some particular regime. In this work, this is achieved with the analytical expression for the optimal protocol that minimizes the…

Statistical Mechanics · Physics 2025-10-03 Pierre Nazé

In this paper the necessary conditions of optimality in the form of maximum principle are derived for a very general class of variational problems. This class includes problems with any optimization criteria and constraints that can be…

Optimization and Control · Mathematics 2009-11-30 Anatoly Tsirlin

We give a proper fractional extension of the classical calculus of variations. Necessary optimality conditions of Euler-Lagrange type for variational problems containing both classical and fractional derivatives are proved. The fundamental…

Optimization and Control · Mathematics 2012-02-28 Tatiana Odzijewicz , Delfim F. M. Torres

This paper provides necessary and sufficient conditions of optimality for variational problems that deal with a fractional derivative with respect to another function. Fractional Euler--Lagrange equations are established for the fundamental…

Optimization and Control · Mathematics 2017-02-06 Ricardo Almeida

Linearized models of power systems are often desirable to formulate tractable control and optimization problems that still reflect real-world physics adequately under various operating conditions. In this paper, we propose an approach that…

Optimization and Control · Mathematics 2018-05-28 Marc Hohmann , Joseph Warrington , John Lygeros

We introduce a new variational characterization of Gaussian diffusion processes as minimum uncertainty states. We then define a variational method constrained by kinematics of diffusions and Schr\"{o}dinger dynamics to seek states of local…

High Energy Physics - Theory · Physics 2016-09-06 F. Illuminati , L. Viola