Error estimates for the finite-element approximation of an elliptic control problem with pointwise state and control constraints
Error estimates for the numerical approximation of semilinear elliptic control problems with finitely many state constraints
The goal of this paper is to derive some error estimates for the numerical discretization of some optimal control problems governed by semilinear elliptic equations with bound constraints on the control and a finitely number of equality and inequality state constraints. We prove some error estimates for the optimal controls in the norm and we also obtain error estimates for the Lagrange multipliers associated to the state constraints as well as for the optimal states and optimal adjoint states....
Error Estimates for the Numerical Approximation of Semilinear Elliptic Control Problems with Finitely Many State Constraints
The goal of this paper is to derive some error estimates for the numerical discretization of some optimal control problems governed by semilinear elliptic equations with bound constraints on the control and a finitely number of equality and inequality state constraints. We prove some error estimates for the optimal controls in the L∞ norm and we also obtain error estimates for the Lagrange multipliers associated to the state constraints as well as for the optimal states and optimal adjoint states. ...
Error-estimates for the Ritz's method of finding eigenvalues and eigenfunctions
Evaluation of Clarke's generalized gradient in optimization of variational inequalities
Evolution of structure for direct control optimization
The paper presents the Monotone Structural Evolution, a direct computational method of optimal control. Its distinctive feature is that the decision space undergoes gradual evolution in the course of optimization, with changing the control parameterization and the number of decision variables. These structural changes are based on an analysis of discrepancy between the current approximation of an optimal solution and the Maximum Principle conditions. Two particular implementations, with spike and...
Evolutionary variational inequalities and applications in plasticity
An abstract theory of evolutionary variational inequalities and its applications to the traction boundary value problems of elastoplasticity are studied, using the penalty method to prove the existence of a solution.
Existence and multiplicity results for homoclinic orbits of Hamiltonian systems.
Existence of solutions for generalized nonlinear mixed variational-like inequalities in Banach spaces.
Exponential stability of nonlinear time-varying differential equations and applications.
Extending the applicability of Newton's method using nondiscrete induction
We extend the applicability of Newton's method for approximating a solution of a nonlinear operator equation in a Banach space setting using nondiscrete mathematical induction concept introduced by Potra and Pták. We obtain new sufficient convergence conditions for Newton's method using Lipschitz and center-Lipschitz conditions instead of only the Lipschitz condition used in F. A. Potra, V. Pták, Sharp error bounds for Newton's process, Numer. Math., 34 (1980), 63–72, and F. A. Potra, V. Pták, Nondiscrete...
External approximation of first order variational problems via W-1,p estimates
Here we present an approximation method for a rather broad class of first order variational problems in spaces of piece-wise constant functions over triangulations of the base domain. The convergence of the method is based on an inequality involving norms obtained by Nečas and on the general framework of Γ-convergence theory.
Extremum theorem and convergence criterion for an iterative solution to the finite-step problem in elastoplasticity with mixed nonlinear hardening
For a class of elastic-plastic constitutive laws with nonlinear kinematic and isotropic hardening, the problem of determining the response to a finite load step is formulated according to an implicit backward difference scheme (stepwise holonomic formulation), with reference to discrete structural models. This problem is shown to be amenable to a nonlinear mathematical programming problem and a criterion is derived which guarantees monotonie convergence of an iterative algorithm for the solution...
Fast level set based algorithms using shape and topological sensitivity information
Fictitious domain/mixed finite element approach for a class of optimal shape design problems
Finding global minima with a filled function approach for non-smooth global optimization.
Finite difference approximation of control via the potential in a 1-D Schrödinger equation.
Finite element approximation of the volume-matching problem.
Finite element error analysis for state-constrained optimal control of the Stokes equations
Finite element estimates for a class of nonlinear variational inequalities.