We consider the class of quadratically-constrained quadratic-programming methods in the framework extended from optimization to more general variational problems. Previously, in the optimization case, Anitescu (SIAM J. Optim. 12, 949–978, 2002) showed superlinear convergence of the primal sequence under the Mangasarian-Fromovitz constraint qualification and the quadratic growth condition. Quadr...

Variational problems for Sobolev maps with bounded total variation that take values into the 1-dimensional projective space are studied. We focus on the different features from the case of Sobolev maps with bounded conformal p-energy that take values into the p-dimensional projective space, for p ≥ 2 integer, recently studied in [18]. In the last decades there has been a growing interest in the...

This paper is dedicated to the analysis of backward stochastic differential equations (BSDEs) with jumps, subject to an additional global constraint involving all the components of the solution. We study the existence and uniqueness of a minimal solution for these so-called constrained BSDEs with jumps via a penalization procedure. This new type of BSDE offers a nice and practical unifying fram...

We study the existence of minimizers for a constrained variational problems in H(R). These minimizers are stable waves solutions for the Generalized Camassa-Holm equation, and their derivative may have a singularity (in which case the travelling wave is called a peakon). The existence result is based on a method developed by the same author in a previous work. By giving examples, we show how ou...

In this paper we study sensitivity analysis of generalized equations (variational inequalities) with nonpolyhedral set constraints. We use an approach of local reduction of the corresponding constraint set to a convex cone. This leads to an introduction of an additional term in a linearization of the generalized equations which represents a curvature of the constraint set. We also discuss conce...

In this paper we consider a new analytic center cutting plane method in a projective space. We prove the eeciency estimates for the general scheme and show that these results can be used in the analysis of a feasibility problem, the variational inequality problem and the problem of constrained minimization. Our analysis is valid even for the problems whose solution belongs to the boundary of th...

We develop and compare multilevel algorithms for solving bound constrained nonlinear variational problems via interior point methods. Several equivalent formulations of the linear systems arising at each iteration of the interior point method are compared from the point of view of conditioning and iterative solution. Furthermore, we show how a multilevel continuation strategy can be used to obt...

Variational Bayesian (VB) inference has become an increasingly popular method for approximating exact in model-based machine learning. The VB approach provides a way to trade off accuracy versus computational complexity and scales better large-dimensional problems than sampling solutions. Julia package ReactiveMP.jl implements automates reactive by minimization of constrained Bethe Free Energy ...

Nonsmooth analysis, inequality constrained optimization and variational inequalities are involved in the modelling of unilateral contact problems. The corresponding theoretical and algorithmic tools, which are part of the area known as nonsmooth mechanics, are by no means classical. In general purpose software some of these tools (perhaps in a simplified way) are currently available. Two engine...