On a SQP-Multigrid Technique for Nonlinear Parabolic Boundary Control Problems

An optimal control problem governed by the heat equation with nonlinear boundary conditions is considered. The objective functional consists of a quadratic terminal part and a quadratic regularization term. It is known, that an SQP method converges quadratically to the optimal solution of the problem. To handle the quadratic optimal control subproblems with high precision, very large scale mathematical programming problems have to be treated. The constrained problem is reduced to an unconstrained one by a method due to Bertsekas. A multigrid approach developed by Hackbusch is applied to solve the unconstrained problems. Some numerical examples illustrate the behaviour of the method. AMS subject classification: 49M40, 49M05 Keywords: optimal control, semilinear parabolic equation, multigrid method, SQP method 1 Introduction The behaviour of Lagrange--Newton--SQP methods for solving nonlinear optimal control problems has been the subject of several recent publications. For instance, th..

Modified mRNA directs the fate of heart progenitor cells and induces vascular regeneration after myocardial infarction

In a cell-free approach to regenerative therapeutics, transient application of paracrine factors in vivo could be used to alter the behavior and fate of progenitor cells to achieve sustained clinical benefits. Here we show that intramyocardial injection of synthetic modified RNA (modRNA) encoding human vascular endothelial growth factor-A (VEGF-A) results in the expansion and directed differentiation of endogenous heart progenitors in a mouse myocardial infarction model. VEGF-A modRNA markedly improved heart function and enhanced long-term survival of recipients. This improvement was in part due to mobilization of epicardial progenitor cells and redirection of their differentiation toward cardiovascular cell types. Direct in vivo comparison with DNA vectors and temporal control with VEGF inhibitors revealed the greatly increased efficacy of pulse-like delivery of VEGF-A. Our results suggest that modRNA is a versatile approach for expressing paracrine factors as cell fate switches to control progenitor cell fate and thereby enhance long-term organ repair.Stem Cell and Regenerative Biolog