In this paper we introduce general prenormal and normal structures in Banach spaces that cover conventional concepts of normals to arbitrary closed sets under minimal requirements. Based on these structures, we establish new abstract versions of the extremal principle in variational analysis, which plays a fundamental role in many applications. The main applications of this paper concern necess...

TO SYMMETRIC VARIATIONAL PROBLEMS Giuseppe Gaeta Department of Mathematical Sciences Loughborough University of Technology Loughborough LE11 3TU (England) [email protected] Summary By combining the Michel's geometric theory of symmetry breaking and classical result from variational analysis, we obtain a lower bound on critical points with given symmetry H G of a potential symmetric under G. The...

We present a new stochastic learning machine for speech separation based on the variational recurrent neural network (VRNN). This VRNN is constructed from the perspectives of generative stochastic network and variational auto-encoder. The idea is to faithfully characterize the randomness of hidden state of a recurrent neural network through variational learning. The neural parameters under this...

This paper discusses a variational method of processing the scanning laser ophthalmoscope(cSLO) image sequences in the context of extracting the local rhodopsin density and modeling the bleaching kinetics. This work supports the characterization and detection of early pathological changes in clinical retinal data. Our goals include providing automated tools for tracing early pathological change...

Recent results about strong metric regularity of solution mappings are applied to a challenging situation in basic mathematical economics, a model of market equilibrium in the exchange of goods. The solution mapping goes from the initial endowments of the agents to the goods they end up with and the supporting prices, and the issue is whether, relative to a particular equilibrium, it has a sing...

generalized resolvent equations; variational inclusions; algorithm; convergence; generalized pseudocontractive mapping

Non-local methods for image denoising and inpainting have gained considerable attention in recent years. This is in part due to their superior performance in textured images and regions, a known weakness of purely local methods. Local methods on the other hand have demonstrated to be very appropriate for the recovering of geometric structure such as image edges. The synthesis of both types of m...

In this research note we provide a variational basis for the optimal artificial diffusion method, which has been a cornerstone in developing many stabilized methods. The optimal artificial diffusion method produces exact nodal solutions when applied to one-dimensional problems with constant coefficients and forcing function. We first present a variational principle for a multi-dimensional advec...

Acknowledgment: We thank Philip D. Loewen for careful and critical reading of an early version of this paper. We also thank Jane J. J. Ye for her comments. Abstract. We provide a reened sensitivity analysis for nite and innnite horizon control problems where in both cases the perturbation space is L 1. Our underlying technique relies on a recent sequential description of both the generalized gr...

The metric subregularity of multifunctions is a key notion in Variational Analysis and Optimization. In this paper, we establish firstly a cretirion for metric subregularity of multifunctions between metric spaces, by using the strong slope. Next, we use a combination of abstract coderivatives and contingent derivatives to derive verifiable first order conditions ensuring the metric subregulari...