Variational approximation methods have become a mainstay of contemporary Machine Learning methodology, but currently have little presence in Statistics. We devise an effective variational approximation strategy for fitting generalized linear mixed models (GLMM) appropriate for grouped data. It involves Gaussian approximation to the distributions of random effects vectors, conditional on the res...

Clustering is an important task in network analysis, with applications in fields such as biology and the social sciences. We present a novel inference algorithm for the Stochastic Block Model (SBM), a well known network clustering model. Previous inference in this model typically utilizes Markov Chain Monte Carlo or Variational Bayes, but our method is the first to utilize Stochastic Variationa...

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...

The applicant develops new tools of variational analysis; in particular, two new versions of the Ekeland variational principle and subdifferential variational principle for set-valued mappings, as well as new constructions of extremal set systems. They play a significant role to studying an important class of constrained optimization problems called Multiobjective Optimization Problems with Equ...

The numerical analysis of variational integrators relies on variational error analysis, which relates the order of accuracy of a variational integrator with the order of approximation of the exact discrete Lagrangian by a computable discrete Lagrangian. The exact discrete Lagrangian can either be characterized variationally, or in terms of Jacobi’s solution of the Hamilton– Jacobi equation. The...

In this paper we introduce and study enhanced notions of relative Pareto minimizers to constrained multiobjective problems that are defined via several kinds of relative interiors of ordering cones and occupy intermediate positions between the classical notions of Pareto and weak Pareto efficiency /minimality. Using advanced tools of variational analysis and generalized differentiation, we esta...

In this paper we introduce and study enhanced notions of relative Pareto minimizers to constrained multiobjective problems that are defined via several kinds of relative interiors of ordering cones and occupy intermediate positions between the classical notions of Pareto and weak Pareto efficiency/minimality. Using advanced tools of variational analysis and generalized differentiation, we estab...

As technology scales down, timing verification of digital integrated circuits becomes an extremely difficult task due to the gate and wire variability. Therefore, statistical timing analysis (denoted by σTA) is becoming unavoidable. In this paper, two new approaches for doing statistical gate timing analysis for Gaussian and non-Gaussian sources of variation in block-based σTA are presented. To...

The expected value of a functional F(η) of a Poisson process η can be considered a function of its intensity measure μ . The paper surveys several results concerning differentiability properties of this functional on the space of signed measures with finite total variation. Then necessary conditions for μ being a local minima of the considered functional are elaborated taking into account possi...

In this paper we study the behavior of the local solutions of perturbed variational inequalities, governed by perturbations to both the variational inequality function and the feasible region. Assuming appropriate second-order and regularity conditions, we show that the perturbed local solution set is nonempty, Lipschitz continuous, and directionally differentiable. Even when the directional di...