The extended variational principle fails for non-holonomic case. We use a vertical rolling disk as an example to illustrate this failure. We have studied the fundamental dynamical principle from which the motion of a mechanical system, whether holonomic or non-holonomic, can be derived.

It is well known that the resolvent equations are equivalent to the extended general mixed variational inequalities. We use this alternative equivalent formulation to study the sensitivity of the extended general mixed variational inequalities without assuming the differentiability of the given data. Since the extended general mixed variational inequalities include extended general variational ...

We introduce and study a new class of general nonlinear implicit variational inequalities, which includes several classes of variational inequalities and variational inclusions as special cases. By applying the resolvent operator technique and fixed point theorem, we suggest a new perturbed three-step iterative algorithm with errors for solving the class of variational inequalities. Several exi...

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...