An implementation of recursive quadratic programming variable metric methods for linearly constrained nonlinear minimax approximation
An implicit extragradient method for hierarchical variational inequalities.
An improved convergence analysis of a superquadratic method for solving generalized equations.
An inexact proximal-type method for the generalized variational inequality in Banach spaces.
An Ishikawa-hybrid proximal point algorithm for nonlinear set-valued inclusions problem based on -accretive framework.
An iterative method for solving the generalized system of relaxed cocoercive quasivariational inclusions and fixed point problems of an infinite family of strictly pseudocontractive mappings.
An L2-Error Estimate for an Approximation of the Solution of a Parabolic Variational Inequality.
An optimization problem in heat conduction
An SQP method for mathematical programs with complementarity constraints with strong convergence properties
We propose an SQP algorithm for mathematical programs with complementarity constraints which solves at each iteration a quadratic program with linear complementarity constraints. We demonstrate how strongly M-stationary solutions of this quadratic program can be obtained by an active set method without using enumeration techniques. We show that all limit points of the sequence of iterates generated by our SQP method are at least M-stationary.
Analysis and finite element error estimates for the velocity tracking problem for Stokes flows via a penalized formulation
A distributed optimal control problem for evolutionary Stokes flows is studied via a pseudocompressibility formulation. Several results concerning the analysis of the velocity tracking problem are presented. Semidiscrete finite element error estimates for the corresponding optimality system are derived based on estimates for the penalized Stokes problem and the BRR (Brezzi-Rappaz-Raviart) theory. Finally, the convergence of the solutions of the penalized optimality systems as is examined.
Analysis and finite element error estimates for the velocity tracking problem for Stokes flows via a penalized formulation
A distributed optimal control problem for evolutionary Stokes flows is studied via a pseudocompressibility formulation. Several results concerning the analysis of the velocity tracking problem are presented. Semidiscrete finite element error estimates for the corresponding optimality system are derived based on estimates for the penalized Stokes problem and the BRR (Brezzi-Rappaz-Raviart) theory. Finally, the convergence of the solutions of the penalized optimality systems as ε → 0 is examined. ...
Application of the optimal control theory to the wastewater elimination problem.
The main goal of this paper is to show some applications of the optimal control theory to the wastewater elimination problem. Firstly, we deal with the numerical simulation of a given situation. We present a suitable mathematical model, propose a method to solve it and show the numerical results for a realistic situation in the ría of Arousa (Spain). Secondly, in the same framework of wastewater elimination problem, we pose two economic-environmental problems which can be formulated as constrained...
Applications of Fixed-Point Methods to Discrete Variational and Quasi-Variational Inequalities.
Approximate gradient projection method with general Runge-Kutta schemes and piecewise polynomial controls for optimal control problems
Approximate maximum principle for discrete approximations of optimal control systems with nonsmooth objectives and endpoint constraints
The paper studies discrete/finite-difference approximations of optimal control problems governed by continuous-time dynamical systems with endpoint constraints. Finite-difference systems, considered as parametric control problems with the decreasing step of discretization, occupy an intermediate position between continuous-time and discrete-time (with fixed steps) control processes and play a significant role in both qualitative and numerical aspects of optimal control. In this paper we derive an...
Approximation d'équations aux dérivées partielles par des méthodes de décomposition
Approximation methods for nonlinear problems with constraints in form of variational inequalities
Approximation numérique des équations Hamilton-Jacobi-Bellman
Approximation of a Martensitic Laminate with Varying Volume Fractions
We give results for the approximation of a laminate with varying volume fractions for multi-well energy minimization problems modeling martensitic crystals that can undergo either an orthorhombic to monoclinic or a cubic to tetragonal transformation. We construct energy minimizing sequences of deformations which satisfy the corresponding boundary condition, and we establish a series of error bounds in terms of the elastic energy for the approximation of the limiting macroscopic deformation and...
Approximation of maximal Cheeger sets by projection
This article deals with the numerical computation of the Cheeger constant and the approximation of the maximal Cheeger set of a given subset of . This problem is motivated by landslide modelling as well as by the continuous maximal flow problem. Using the fact that the maximal Cheeger set can be approximated by solving a rather simple projection problem, we propose a numerical strategy to compute maximal Cheeger sets and Cheeger constants.