Variational analysis concerns the geometry and calculus of nonsmooth sets and functions, often viewed from an optimization perspective. Over several decades, variational analysis has matured into a powerful and elegant theory. One rich source of concrete examples involves the eigenvalues of symmetric and nonsymmetric matrices, sometimes deriving from dynamical or feedback control questions. Thi...

We examine a variational problem from elastic stability theory: a thin elastic strut on an elastic foundation. The strut has infinite length, and its lateral deflection is represented by u : R→ R. Deformation takes place under conditions of prescribed total shortening, leading to the variational problem inf { 1 2 ∫ u′′ 2 + ∫ F (u) : 1 2 ∫ u′ 2 = λ } . (0.1) Solutions of this minimization proble...

The paper is devoted to optimization problems of the Bolza and Mayer types for evolution systems governed by nonconvex Lipschitzian differential inclusions in Banach spaces under endpoint constraints described by finitely many equalities and inequalities. with generally nonsmooth functions. We develop a variational analysis of such problems mainly based on their discrete approximations and the ...

In this paper the standard variational analysis scheme is modified, through a simple transform, to avoid the inversion of the background error covariance matrix. A close inspection of the modified scheme reveals that it is possible to use a filter to replace the multiplication of the covariance matrix. A variational analysis scheme using a filter is then formulated, which does not explicitly in...

We present deep variational canonical correlation analysis (VCCA), a deep multiview learning model that extends the latent variable model interpretation of linear CCA (Bach and Jordan, 2005) to nonlinear observation models parameterized by deep neural networks (DNNs). Computing the marginal data likelihood, as well as inference of the latent variables, are intractable under this model. We deriv...

in this work, the blasius equation is studied. homotopy perturbation method (hpm) and homotopy analysis method (ham) are applied to obtain its solution. comparison with variational iteration method (vim) is made to highlight the significant features of employed methods and their capability of handling nonlinear problems. the outcome shows the success of (hpm) and (ham) for solving nonlinear pro...

In this paper, we introduce and study a mixed variational inclusion problem involving infinite family of fuzzy mappings. An iterative algorithm is constructed for solving a mixed variational inclusion problem involving infinite family of fuzzy mappings and the convergence of iterative sequences generated by the proposed algorithm is proved. Some illustrative examples are also given.

‎in this paper‎, ‎we introduce and study a class of generalized vector quasi-equilibrium problem‎, ‎which includes many vector equilibrium problems‎, ‎equilibrium problems‎, ‎vector variational inequalities and variational inequalities as special cases‎. ‎using one person game theorems‎, ‎the concept of escaping sequences and without convexity assumptions‎, ‎we prove some existence results for ...

The paper is devoted to applications of advanced tools of modern variational analysis and generalized differentiation to problems of optimistic bilevel programming. In this way, new necessary optimality conditions are derived for two major classes of bilevel programs: those with partially convex and with fully convex lower-level problems. We provide detailed discussions of the results obtained ...

We use variational methods to provide a concise development of a number of basic results in convex and functional analysis. This illuminates the parallels between convex analysis and smooth subdifferential theory. 1. The purpose of this note is to give a concise and explicit account of the following folklore: several fundamental theorems in convex analysis such as the sandwich theorem and the F...