Abstract. This paper provides a detailed analysis of a primal-dual interior-point method for PDE-constrained optimization. Considered are optimal control problems with control constraints in L. It is shown that the developed primal-dual interior-point method converges globally and locally superlinearly. Not only the easier L-setting is analyzed, but also a more involved L-analysis, q < ∞, is pr...

Statistical tomographic reconstruction algorithms generally require the efficient optimization of a functional. A recent algorithm known as iterative coordinate descent with Newton-Raphson updates (ICD/NR) has been shown to be much more computationally efficient than indirect optimization approaches based on the EM algorithm. However, while the ICD/NR algorithm has experimentally been shown to ...

Optimization of convex functions subject to eigenvalue constraints is intriguing because of peculiar analytical properties of eigenvalue functions and is of practical interest because of a wide range of applications in fields such as structural design and control theory. Here we focus on the optimization of a linear objective subject to a constraint on the smallest eigenvalue of an analytic and...

In the first part of the present paper, we investigated stability and convergence of a new direct linear adaptive neural network intended for separating independent sources when it is controlled by the well-known Hérault–Jutten algorithm. In this second part, we study the corresponding feedback adaptive network. For two globally sub-Gaussian sources, the network achieves quasiconvergence in the...

This study examines the role of tourism development in reducing regional income inequality in China. First, the theoretical foundation for how tourism affects regional income inequality is discussed. Second, based on the conditional convergence framework, this study proposes a spatiotemporal autoregressive model to capture spatial and temporal dependence as well as spatial heterogeneity. Touris...

This paper is concerned with the stability and approximation properties of enriched meshfree methods. In particular we focus on the particle-partition of unity method (PPUM) yet the presented results hold for any partition of unity based enrichment scheme. The goal of our enrichment scheme is to recover the optimal convergence rate of the uniform h-version independent of the regularity of the s...

In a recent paper [11], Vishik proved the global well-posedness of the two-dimensional Euler equation in the critical Besov space B 2,1. In the present paper we prove that Navier-Stokes system is globally well-posed in B 2,1, with uniform estimates on the viscosity. We prove also a global result of inviscid limit. The convergence rate in L is of order ν. keywords. navier-Stokes equations; Incom...