33 research outputs found
Lie symmetry and conservation laws for magneto-static magnetic shape memory alloys system
Approximation of solutions to second order nonlinear Picard problems with Carathéodory right-hand side
State Dependent Sweeping Process in p-Uniformly Smooth and q-Uniformly Convex Banach Spaces
On the Correctness of the Well-Known Mathematical Model of Irradiation-Induced Swelling with the Influence of Stresses in the Problems of Elastic-Plastic Deformation Mechanics
On A Nonsmooth Newton Method For Nonlinear Complementarity Problems In Function Space With Applications To Optimal Control
Many applications in mathematical modeling and optimal control lead to problems that are posed in function spaces and contain pointwise complementarity conditions. In this paper, a projected Newton method for nonlinear complementarity problems in the innite dimensional function space L p is proposed and analyzed. Hereby, an NCP-function is used to reformulate the problem as a nonsmooth operator equation. The method stays feasible with respect to prescribed bound-constraints. The convergence analysis is based on semismoothness results for superposition operators in function spaces. The proposed algorithm is shown to converge locally q-superlinearly to a regular solution. As an important tool for applications, we establish a sufficient condition for regularity. The application of the algorithm to the distributed bound-constrained control of an elliptic partial dierential equation is discussed in detail. Numerical results confirm the efficiency of the method