The shrinking projection method for solving variational inequality problems and fixed point problems in Banach spaces.
The singular set of the minima of certain quadratic functionals
The solution of a minimax problem connected to the irreducibility of polynominals.
The solution of two-point boundary value problem of a class of Duffing-type systems with non- perturbation term.
The solvability of a new system of nonlinear variational-like inclusions.
The spectrum of the damped wave operator for a bounded domain in .
The SQP method for control constrained optimal control of the Burgers equation
A Lagrange–Newton–SQP method is analyzed for the optimal control of the Burgers equation. Distributed controls are given, which are restricted by pointwise lower and upper bounds. The convergence of the method is proved in appropriate Banach spaces. This proof is based on a weak second-order sufficient optimality condition and the theory of Newton methods for generalized equations in Banach spaces. For the numerical realization a primal-dual active set strategy is applied. Numerical examples are...
The SQP method for control constrained optimal control of the Burgers equation
A Lagrange–Newton–SQP method is analyzed for the optimal control of the Burgers equation. Distributed controls are given, which are restricted by pointwise lower and upper bounds. The convergence of the method is proved in appropriate Banach spaces. This proof is based on a weak second-order sufficient optimality condition and the theory of Newton methods for generalized equations in Banach spaces. For the numerical realization a primal-dual active set strategy is applied. Numerical examples are...
The structure and limiting behavior of locally optimal minimizers
The structure of extremals of a class of second order variational problems
The structure of the critical set in the general mountain pass principle
The sufficient condition for linear constant time-lag systems to be normal systems
The system of generalized set-valued equilibrium problems.
The union of uniform closed balls conjecture
The use of monotone norms in epigraphical analysis.
The use of Young measures for constructing minimizing sequences in the calculus of variations.
The value function representing Hamilton–Jacobi equation with hamiltonian depending on value of solution
In the paper we investigate the regularity of the value function representing Hamilton–Jacobi equation: − Ut + H(t, x, U, − Ux) = 0 with a final condition: U(T,x) = g(x). Hamilton–Jacobi equation, in which the Hamiltonian H depends on the value of solution U, is represented by the value function with more complicated structure than the value function in Bolza problem. This function is described with the use of some class of Mayer problems related to the optimal control theory and the calculus of...
The variational contact problem for elastic objects of different dimensions.
The viscosity subdifferential of the sum of two functions in Banach spaces. I: First order case.
The von Neumann minimax theorem revisited