Second-Order Variational Analysis of Parametric Constraint and Variational Systems

Robinson Stability of Parametric Constraint Systems via Variational Analysis

Hölder continuity of a parametric variational inequality

‎In this paper‎, ‎we study the Hölder continuity of solution mapping to a parametric variational inequality‎. ‎At first‎, ‎recalling a real-valued gap function of the problem‎, ‎we discuss the Lipschitz continuity of the gap function‎. ‎Then under the strong monotonicity‎, ‎we establish the Hölder continuity of the single-valued solution mapping for the problem‎. ‎Finally‎, ‎we apply these resu...

Second-order stochastic variational inference

Stochastic gradient descent (SGD), the workhorse of stochastic optimization, is slow in theory (sub-linear convergence) and in practice (thousands of iterations), intuitively for two reasons: 1) Its learning rate schedule is fixed a priori and decays rapidly enough to 0 that is square-summable. This learning rate schedule limits the step size and hence the rate of convergence for a Lipschitz ob...

Second Order Variational Optic Flow Estimation

In this paper we present a variational approach to accurately estimate the motion vector field in a image sequence introducing a second order Taylor expansion of the flow in the energy function to be minimized. This feature allows us to simultaneously obtain, in addition, an estimation of the partial derivatives of the motion vector field. The performance of our approach is illustrated with the...

Parametric variational principle and residuality

We prove a parametric version of a smooth convex variational principle with constraints using a Baire category approach. We examine in depth the necessity of the assumptions of our variational principle by providing counterexamples.