O jistém zobecnění Picard-Lindelöfovy metody postupných aproximací řešení diferenciální rovnice
On a method of optimization
On an iterative method for variational inequalities.
On an optimal control problem for a quasilinear parabolic equation
An optimal control problem governed by a quasilinear parabolic equation with additional constraints is investigated. The optimal control problem is converted to an optimization problem which is solved using a penalty function technique. The existence and uniqueness theorems are investigated. The derivation of formulae for the gradient of the modified function is explainedby solving the adjoint problem.
On discrete control problems having a minmax type objective functional
On existence of solutions to degenerate nonlinear optimization problems
We investigate the existence of the solution to the following problem min φ(x) subject to G(x)=0, where φ: X → ℝ, G: X → Y and X,Y are Banach spaces. The question of existence is considered in a neighborhood of such point x₀ that the Hessian of the Lagrange function is degenerate. There was obtained an approximation for the distance of solution x* to the initial point x₀.
On integral representation, relaxation and homogenization for unbounded functionals
A theory of integral representation, relaxation and homogenization for some types of variational functionals taking extended real values and possibly being not finite also on large classes of regular functions is presented. Some applications to gradient constrained relaxation and homogenization problems are given.
On numerical approximation of an optimal control problem in linear elasticity.
On Optimal Spectral Estimator for Multi-Dimensional Time Series with an Infinite Number of Sample Points.
On perturbations of minimum problems with unbounded controls.
On primal-dual stability in convex optimization.
On regularization methods for the numerical solution of parabolic control problems with pointwise state constraints
In this paper we study Lavrentiev-type regularization concepts for linear-quadratic parabolic control problems with pointwise state constraints. In the first part, we apply classical Lavrentiev regularization to a problem with distributed control, whereas in the second part, a Lavrentiev-type regularization method based on the adjoint operator is applied to boundary control problems with state constraints in the whole domain. The analysis for both classes of control problems is investigated and...
On regularization methods for the numerical solution of parabolic control problems with pointwise state constraints
In this paper we study Lavrentiev-type regularization concepts for linear-quadratic parabolic control problems with pointwise state constraints. In the first part, we apply classical Lavrentiev regularization to a problem with distributed control, whereas in the second part, a Lavrentiev-type regularization method based on the adjoint operator is applied to boundary control problems with state constraints in the whole domain. The analysis for both classes of control problems is investigated and...
On superlinear multiplier update methods for partial augmented Lagrangian techniques.
The minimization of a nonlinear function with linear and nonlinear constraints and simple bounds can be performed by minimizing an augmented Lagrangian function, including only the nonlinear constraints. This procedure is particularly interesting in case that the linear constraints are flow conservation equations, as there exist efficient techniques to solve nonlinear network problems. It is then necessary to estimate their multipliers, and variable reduction techniques can be used to carry out...
On the boundary element method for the Signorini problem of the Laplacian.
On the Convergence of an Inverse Iteration Method for Nonlinear Elliptic Eigenvalue Problems.
On the convergence of min/sup points in optimal control problems.
On the Convergence of the Approximate Free Boundary for the Parabolic Obstacle Problem
Si discretizza il problema dell'ostacolo parabolico con differenze all'indietro nel tempo ed elementi finiti lineari nello spazio e si dimostrano stime dell'errore per la frontiera libera discreta.
On the Efficient Solution of Nonlinear Finite Element Equations. II. Bound-Constrained Problems.
On the Efficient Solution of Nonlinear Finite Element Equations I.