We consider the coupling of compressible and nearly incompressible materials within the framework of mortar methods. Taking into account the locking effect, we use a suitable discretization for the nearly incompressible material and work with a standard conforming discretization elsewhere. The coupling of different discretization schemes in different subdomains are handled by flexible mortar te...

In this talk, we extend our investigations on interior point methods for elliptic state-constrained optimal control problems in [4] and [2] to the parabolic case. The main difficulty of the numerical analysis of interior point methods for such problems is the lack of regularity of Lagrange multipliers associated with the state constraints. Therefore, it is helpful to improve the properties of t...

This work is devoted to stationary optimal control problems with polygonal constraints on the components of the state. Existence of Lagrange multipliers, of different regularity, is verified for the cases with and without Slater condition holding. For the numerical realization a semi-smooth Newton method is proposed for an appropriately chosen family of regularized problems. The asymptotic beha...

This work is devoted to stationary optimal control problems with polygonal constraints on the components of the state. Existence of Lagrange multipliers, of different regularity, is verified for the cases with and without Slater condition holding. For the numerical realization a semi-smooth Newton method is proposed for an appropriately chosen family of regularized problems. The asymptotic beha...

We study the five-dimensional supergravity dual of the a-maximization under AdS5/CFT4 duality. We firstly show that the a-maximization is mapped to the attractor equation in five-dimensional gauged supergravity, and that the trial a-function is the inverse cube of the superpotential of the five-dimensional theory. There is also a version of a-maximization in which one extremizes over Lagrange m...

This paper deals with an algorithm which incorporates the interior point method into the Dantzig-Wolfe decomposition technique for solving large-scale linear programming problems. At each iteration, the algorithm performs one step of Newton's method to solve a subproblem, obtaining an approximate solution, which is then used to compute an approximate Newton direction to nd a new vector of the L...