In many data mining applications, the data manifold is of lower dimension than the dimension of the input space. In this paper, it is proposed to take advantage of this additional information in the frame of variational mixtures. The responsibilities computed in the VBE step are constrained according to a discrepancy measure between the Euclidean and the geodesic distance. The methodology is ap...

By using appropriate methods of variational analysis, the necessary conditions optimality are established for new classes constrained optimization problems involving multiple and curvilinear integral functionals. Additionally, two illustrative examples provided to support main results formulated in this paper.

Variational problems and the solvability of certain nonlinear equations have a long and rich history beginning with calculus and extending through the calculus of variations. In this paper, we are interested in ‘well-connected’ pairs of such problems which are not necessarily related by critical point considerations. We also study constrained problems of the kind which arise in mathematical pro...

We present local convergence analysis of the method of multipliers for equality-constrained variational problems (in the special case of optimization, also called the augmented Lagrangian method) under the sole assumption that the dual starting point is close to a noncritical Lagrange multiplier (which is weaker than second-order sufficiency). Local superlinear convergence is established under ...

This is the first paper dealing with the study of weak sharp minima for constrained optimization problems on Riemannian manifolds, which are important in many applications. We consider the notions of local weak sharp minima, boundedly weak sharp minima, and global weak sharp minima for such problems and establish their complete characterizations in the case of convex problems on finite-dimensio...