In this paper, we consider a new class of quasi variational inequalities involving three operators, which is called the extended general quasi variational inequality. It is shown that the extended general quasi variational inequalities are equivalent to the fixed problems. This equivalence is used to suggest and analyze some iterative methods for solving the extended general quasi variational i...

We propose a black-box variational inference method to approximate intractable distributions with an increasingly rich approximating class. Our method, variational boosting, iteratively refines an existing variational approximation by solving a sequence of optimization problems, allowing a trade-off between computation time and accuracy. We expand the variational approximating class by incorpor...

We use the auxiliary principle technique to suggest and analyze some iterative methods for solving a new class of variational inequalities, which is called the mixed trifunction variational inequality. The mixed trifunction variational inequality includes the trifunction variational inequalities and the classical variational inequalities as special cases. Convergence of these iterative methods ...

This paper aims to present a structured variational inference algorithm for switching linear dynamical systems (SLDSs) which was initially introduced by Pavlovic and Rehg [14]. Starting with the need for the variational approach, we proceed to the derivation of the generic (model-independent) variational update formulas which are obtained under the mean field assumption. This leads us to the de...

We introduce and study a new system of variational inclusions with (H ,η)-accretive operators, which contains variational inequalities, variational inclusions, systems of variational inequalities, and systems of variational inclusions in the literature as special cases. By using the resolvent technique for the (H ,η)-accretive operators, we prove the existence and uniqueness of solution and the...

We introduce and study a class of η-generalized vector variational-like inequalities and a class of ηgeneralized strong vector variational-like inequalities in the setting of Hausdorff topological vector spaces. An equivalence result concerned with two classes of η-generalized vector variational-like inequalities is proved under suitable conditions. By using FKKM theorem, some new existence res...

in this paper, we establish an existence result of the solution for an generalized strong vector variational inequality already considered in the literature and as applications we obtain a new coincidence point theorem in hilbert spaces.

Bayesian learning is widely used in many applied datamodelling problems and is often accompanied with approximation schemes since it requires intractable computation of the posterior distributions. In this study, we focus on the two approximation methods, the variational Bayes and the local variational approximation. We show that the variational Bayes approach for statistical models with latent...

A brief introduction to discrete variational mechanics, motivated by the goal of constructing symplectic onestep methods, will be presented. Followed by the presentation of a new type of variational integrator that utilizes Taylor’s method in it’s construction. Time permitting, we will make some remarks on the pros/cons and stability of constructing the variational integrator from the Lagrangia...