The penalty method for a new system of generalized variational inequalities.
The periodic unfolding method in perforated domains.
The perturbed generalized proximal point algorithm
The plenary hull of the generalized Jacobian matrix and the inverse function theorem in subdifferential calculus
The problem of the number of switches in parabolic equations with control
The quadratic criterion of control process quality using the exponential weighting function
The regularity of the trace for minimal surfaces
The relaxation of the Signorini problem for polyconvex functionals with linear growth at infinity
The aim of this paper is to study the unilateral contact condition (Signorini problem) for polyconvex functionals with linear growth at infinity. We find the lower semicontinuous relaxation of the original functional (defined over a subset of the space of bounded variations BV(Ω)) and we prove the existence theorem. Moreover, we discuss the Winkler unilateral contact condition. As an application, we show a few examples of elastic-plastic potentials for finite displacements.
The relaxed energy for -valued maps and measurable weights
The second order optimality conditions for nonlinear mathematical programming with data
To find nonlinear minimization problems are considered and standard -regularity assumptions on the criterion function and constrained functions are reduced to -regularity. With the aid of the generalized second order directional derivative for real-valued functions, a new second order necessary optimality condition and a new second order sufficient optimality condition for these problems are derived.
The shooting approach in analyzing bang-bang extremals with simultaneous control switches
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