In this paper, we introduce and consider a new class of variational inequalities involving two operators, which is called the general nonconvex quasi variational inequality. Several special cases are discussed. We use the projection technique to establish the equivalence between the general nonconvex quasi variational inequalities and the fixed point problems. This alternative equivalent formul...

In this paper, a class of generalized general mixed quasi variational inequalities is introduced and studied. We prove the existence of the solution of the auxiliary problem for the generalized general mixed quasi variational inequalities, suggest a predictor-corrector method for solving the generalized general mixed quasi variational inequalities by using the auxiliary principle technique. If ...

In this paper, a class of mixed inverse variational inequalities is introduced and studied. We prove the existence of the solution of the auxiliary problem for mixed inverse variational inequalities, suggest a predictor-corrector method for solving the mixed inverse variational inequalities by using the auxiliary principle technique. Then it is shown that the convergence of the new method requi...

Gaussian process latent variable models (GPLVMs) are a probabilistic approach to modelling data that employs Gaussian process mapping from latent variables to observations. This paper revisits a recently proposed variational inference technique for GPLVMs and methodologically analyses the optimality and different parameterisations of the variational approximation. We investigate a structured va...

In this paper, we introduce a new class of variational inclusions involving three operator. Using the resolvent operator technique, we establish the equivalence between the general variational inclusions and the resolvent equations. We use this alternative equivalent formulation to suggest and analyze some iterative methods for solving the general variational inclusions. We also consider the cr...

In this paper, we introduce a new class of bifunction variational inequalities, which is called the multivalued mixed quasi bifunction variational inequalities. Using the auxiliary principle technique, we suggest and analyze a proximal point method for solving the multivalued mixed quasi bifunction variational inequalities. It is shown that the convergence of the proposed method requires only p...

A wide variety of Dirichlet-multinomial ‘topic’ models have found interesting applications in recent years. While Gibbs sampling remains an important method of inference in such models, variational techniques have certain advantages such as easy assessment of convergence, easy optimization without the need to maintain detailed balance, a bound on the marginal likelihood, and side-stepping of is...