Abstract not found

We propose a new globalization strategy for primal-dual interior-point methods in nonlinear programming that relaxes the requirement of closely following the central path and lends itself to dynamic updates of the barrier parameter. The latter promote better synchonization between the barrier parameter and the optimality residual, and increase robustness. Global convergence is proved under mild assumptions. We show that the unit Newton step is asymptotically accepted and that linear or superlinear convergence occurs when the barrier parameter goes to zero linearly or superlinearly. Numerical experiments illustrate our results.

Abstract: Microfluidic biochips are devices that are designed for high throughput screening and hybridization in genomics, protein profiling in proteomics, and cell analysis in cytometry. They are used in clinical diagnostics, pharmaceutics and forensics. The biochips consist of a lithographically produced network of channels and reservoirs on top of a glass or plastic plate. The idea is to transport the injected DNA or protein probes in the amount of nanoliters along the network to a reservoir where the chemical analysis is performed. Conventional biochips use external pumps to generate the fluid flow within the network. A more precise control of the fluid flow can be achieved by piezoelectrically agitated surface acoustic waves (SAW) generated by interdigital transducers on top of the chip, traveling across the surface and entering the fluid filled channels. The fluid and SAW interaction can be described by a mathematical model which consists of a coupling of the piezoelectric equations and the compressible Navier-Stokes equations featuring processes that occur on vastly different time scales. In this contribution, we follow a homogenization approach in order to cope with the multiscale behavior of the coupled system that enables a separate treatment of the fast and slowly varying processes. The resulting model equations are the