We establish a semi-group solution concept for morphological differential equations, such as the mean curvature flow equation. The proposed method consists in generating flows from generalized minimizers of nonconvex energy functionals. We use relaxation and convexification to define generalized minimizers. The main part of this work consists in verification of the solution concept by comparing...

in the most described maximum power point tracking (mppt) methods in the literatures, the optimal operation point of the photovoltaic (pv) systems is estimated by linear approximations. however, these approximations can lead to less optimal operating conditions and significantly reduce the performances of the pv systems. this paper proposes a new approach to determine the maximum power point (m...

Unstructured tetrahedral grids are a common data representation of three-dimensional scalar fields. For convex unstructured meshes efficient rendering methods are known. For concave or cyclic meshes, however, a significant overhead is required to sort the grid cells in back to front order. In this paper we apply methods known from computational geometry to transform concave into convex grids. W...

We address here a class of particularly hard-to-solve combinatorial optimization problems namely multicommodity network optimization when the link cost functions are discontinuous step increasing. The main focus is on the development of relaxations for such problems in order to derive lower bounds. A straightforward way of getting lower bounds is to solve the “convexification” of the problem, i...

We consider a class of finite time horizon optimal control problems for continuous time linear systems with a convex cost, convex state constraints and non-convex control constraints. We propose a convex relaxation of the non-convex control constraints, and prove that the optimal solution of the relaxed problem is also an optimal solution for the original problem, which is referred to as the lo...

To exploit the potential of reconfigurable intelligent surface (RIS) in supporting integrated sensing and communication (ISAC), this paper proposes a novel joint active passive beamforming design for RIS-enabled ISAC system consideration target size. First, detection probability is derived closed-form based on illumination power an approximated scattering area target, new concept ultimate resol...

In this contribution we address the efficient solution of optimal control problems of dynamic processes with many controls. Such problems typically arise from the convexification of integer control decisions. We treat this problem class using the direct multiple shooting method to discretize the optimal control problem. The resulting nonlinear problems are solved using an SQP method. Concerning...