arXiv subjects

Fabio Silva Botelho

Publications and source records attributed to Fabio Silva Botelho.

12 recordsLinked to original sources

arXiv2023

On Lagrange multiplier theorems for non-smooth optimization for a large class of variational models in Banach spaces

This article develops optimality conditions for a large class of non-smooth variational models. The main results are based on standard tools of functional analysis and calculus of variations. Firstly we address a model with equality constraints and, in a second step, a more general model with equality and inequality constraints, always in a general Banach space context. We highlight the results in general are well known, however, some novelties are introduced related to the proof procedures, which are in general softer than those concerning the present literature.

math.FA↗

arXiv2022

Dual variational formulations for a large class of non-convex models in the calculus of variations

This article develops dual variational formulations for a large class of models in variational optimization. The results are established through basic tools of functional analysis, convex analysis and duality theory. The main duality principle is developed as an application to a Ginzburg-Landau type system in superconductivity in the absence of a magnetic field. In the first part final sections, we develop new general dual convex variational formulations, more specifically, dual formulations with a large region of convexity around the critical points which are suitable for the non-convex optimization for a large class of models in physics and engineering. Finally, in the last section we present some numerical results concerning the generalized method of lines applied to a Ginzburg-Landau type equation.

math.OC↗

arXiv2022

An approximate proximal numerical procedure concerning the generalized method of lines

This article develops an approximate proximal approach for the generalized method of lines. The present results are extensions and applications of previous ones which have been published since 2011, in books and articles such as [3,4,5,6]. We also recall that in the generalized method of lines, the domain of the partial differential equation in question is discretized in lines (or in curves) and the concerning solution is developed on these lines, as functions of the boundary conditions and the domain boundary shape.

math.GM↗

arXiv2022

A convex dual formulation for a large class of non-convex models in variational optimization

This short communication develops a convex dual variational formulation for a large class of models in variational optimization. The results are established through basic tools of functional analysis, convex analysis and duality theory. The main duality principle is developed as an application to a Ginzburg-Landau type system in superconductivity in the absence of a magnetic field.

math.OC↗

arXiv2021

An approximate numerical method for ordinary differential equation systems with applications to a flight mechanics model

This short communication develops a new numerical procedure suitable for a large class of ordinary differential equation systems found in models in physics and engineering. The main numerical procedure is analogous to those concerning the generalized method of lines, originally published in the here referenced books of 2011 and 2014, [3,5], respectively. Finally, in the last section, we apply the method to a model in flight mechanics.

math.GM↗

arXiv2021

A convex dual variational formulation for non-convex optimization applied to a non-linear model of plates

This article develops duality principles applicable to the non-linear Kirchhoff-Love model of plates. The results are obtained through standard tools of convex analysis, functional analysis, calculus of variations and duality theory. The main duality principle concerns a convex (in fact concave) dual variational formulation and related new optimality conditions for the model in question. Finally, in the last section we develop some global existence results for a similar model in elasticity.

math.OC↗

arXiv2021

A primal dual formulation through a proximal approach for non-convex variational optimization

This article develops a primal dual formulation for a primal proximal approach suitable for a large class of non-convex models in the calculus of variations. The results are established through standard tools of functional analysis, convex analysis and duality theory and are applied to a Ginzburg-Landau type model. Finally, in the last two sections, we present concerning optimal conditions and another related duality principle for the model in question.

math.OC↗

arXiv2021

On duality principles for non-convex optimization with applications to superconductivity and some existence results for a model in non-linear elasticity

This article develops duality principles applicable to the Ginzburg-Landau system in superconductivity. The main results are obtained through standard tools of convex analysis, functional analysis, calculus of variations and duality theory. In the second section, we present the general result for the case including a magnetic field and the respective magnetic potential in a local extremal context. Finally, in the last section we develop some global existence results for a model in elasticity.

math.AP↗

arXiv2020

A note on the Korn inequality in a n-dimensional context

In this short communication, we present a new proof for the Korn inequality in a n-dimensional context. The results are based on standard tools of real and functional analysis. For the final result the standard Poincaré inequality plays a fundamental role.

math.CA↗

arXiv2020

A generalization of the Ekeland variational principle

In this short communication, we present a generalization of the Ekeland variational principle. The main result is established through standard tools of functional analysis and calculus of variations. The novelty here is a result involving the second Gâteaux variation of the functional in question.

math.FA↗

arXiv2020

Optimal control for the nonlinear Fisher-Kolmogorov system with applications to aquatic plant management

Spatiotemporal dynamics of populations may be described by the reaction-diffusion Fisher-Kolmogorov model. In this work we have proposed a new formulation for a control problem of aquatic plants in a temporal dynamics. The solution of this problem is extended to a spatiotemporal Fisher-Kolmogorov system with multiple species of plants interacting in the same place. The control consists on human intervention as a strategy for management of the aquatic plants. In our applications, one plant and two plants cases have been considered. Simulation results are presented to show the effectiveness of the proposed control strategies.

math.OC↗

arXiv2019

A numerical method for an inverse optimization problem through the generalized method of lines

This article develops a solution for an inverse problem through the generalized method of lines. We consider a Laplace equation on a domain with internal and external boundaries with standard Dirichlet boundary conditions. Also, we specify a third non-homogeneous Newmann type boundary condition for the external boundary, and consider the problem of finding the optimal shape for the internal boundary such that all the prescribed boundary conditions are satisfied. The novelty here presented is the application of the generalized method of lines as a tool to compute a solution for such an inverse optimization problem.

math.OC↗