In this paper, we establish a new version of Ekeland’s variational principle in a new setting of cone pseudo-quasimetric spaces. In constrast to metric spaces, we do not require that each forward Cauchy sequence is forward convergent and that each forward convergent sequence has the unique forward limit. The motivation of this paper comes from applications in Behavioral Sciences since a cone ps...

The high-frequency performance of the reflector antennas is mainly limited by the surface. It has been shown that distortions on different regions of the reflector surface can have different effects on the radiation performance. In other words, degradation of the radiation pattern due to the presence of surface distortions is sensitive to the location and behavior of the surface distortion prof...

we establish a relationship between general constrained pseudoconvex optimization problems and globally projected dynamical systems. a corresponding novel neural network model, which is globally convergent and stable in the sense of lyapunov, is proposed. both theoretical and numerical approaches are considered. numerical simulations for three constrained nonlinear optimization problems a...

Integral and integro-differential equations are one of the most useful mathematical tools in both pure and applied mathematics. In this article, we present a variational iteration method for solving Fredholm integro-differential equations. This study provides an analytical approximation to determine the behavior of the solution. To show the efficiency of the present method for our proble...

The analysis of the connections among generalized systems, Vector Optimization Problems and Variational Inequalities allows to deepen the study of the properties of the Minty Vector Variational Inequality. In particular, under suitable regularity assumptions,the equivalence between Minty Vector Variational Inequality and Stampacchia Vector Variational Inequality is shown.

Atar, Chowdhary and Dupuis have recently exhibited a variational formula for exponential integrals of bounded measurable functions in terms of Rényi divergences. We develop a variational characterization of the Rényi divergences between two probability distributions on a measurable space in terms of relative entropies. When combined with the elementary variational formula for exponential integr...

Recent advances in variational and optimization methods applied to increasingly complex numerical weather prediction models with larger numbers of degrees of freedom mandate to take a perspective view of past and recent developments in this field, and present a view of the state of art in the field. Variational methods attempt to achieve a best fit between data and model subject to some ‘a prio...

1. Variational inference and learning We derive the variational inference updates in this section. We use these updates as an E-step in a variational EM framework that is guaranteed to increase a lower bound on the data likelihood. The variational inference updates for our Q-distributions are given below.

This thesis is concerned with state estimation in partially observed diffusion processes with discrete time observations. This problem can be solved exactly in a Bayesian framework, up to a set of generally intractable stochastic partial differential equations. Numerous approximate inference methods exist to tackle the problem in a practical way. This thesis introduces a novel deterministic app...

We review three algorithms for Latent Dirichlet Allocation (LDA). Two of them are variational inference algorithms: Variational Bayesian inference and Online Variational Bayesian inference and one is Markov Chain Monte Carlo (MCMC) algorithm – Collapsed Gibbs sampling. We compare their time complexity and performance. We find that online variational Bayesian inference is the fastest algorithm a...