Related papers: Some reflections on variational methods for partia…

Variable projection solves structured optimization problems by completely minimizing over a subset of the variables while iterating over the remaining variables. Over the last 30 years, the technique has been widely used, with empirical and…

In recent years, sparse spectral methods for solving partial differential equations have been derived using hierarchies of classical orthogonal polynomials on intervals, disks, disk-slices and triangles. In this work we extend the…

Convergence results are stated for the variational iteration method applied to solve an initial value problem for a system of ordinary differential equations.

In a previous article by the author, it was shown that one could effectively give a variational formulation to non-conservative mechanical systems by starting with the first variation functional instead of an action functional. In this…

Using a variational technique, we generalize the statistical physics approach of learning from random examples to make it applicable to real data. We demonstrate the validity and relevance of our method by computing approximate estimators…

This article considers some classes of models dealing with the dynamics of discrete curves subjected to stochastic deformations. It turns out that the problems of interest can be set in terms of interacting exclusion processes, the ultimate…

Variational quantum metrology represents a powerful tool for optimizing generic estimation strategies, combining the principles of variational optimization with the techniques of quantum metrology. Such optimization procedures result…

Intractable distributions present a common difficulty in inference within the probabilistic knowledge representation framework and variational methods have recently been popular in providing an approximate solution. In this article, we…

The paper explores the differential inclusion of a special form. It is supposed that the support function of the set in the right-hand side of an inclusion may contain the sum of the maximum and the minimum of the finite number of…

Motivated by recent developments in Hamiltonian variational principles, Hamiltonian variational integrators, and their applications such as to optimization and control, we present a new Type II variational approach for Hamiltonian systems,…

We construct several variational integrators--integrators based on a discrete variational principle--for systems with Lagrangians of the form L = L_A + epsilon L_B, with epsilon << 1, where L_A describes an integrable system. These…

We propose a method for variable selection in discriminant analysis with mixed categorical and continuous variables. This method is based on a criterion that permits to reduce the variable selection problem to a problem of estimating…

In this talk we go over several new developments regarding the techniques for a large class of non-hermitian matrix models with unitary randomness (complex random numbers). In particular, we discuss: (a) - A diagrammatic approach based on a…

Recently, fractional differential equations have been investigated via the famous variational iteration method. However, all the previous works avoid the term of fractional derivative and handle them as a restricted variation. In order to…

This paper introduces weighted finite difference methods for numerically solving dispersive evolution equations with solutions that are highly oscillatory in both space and time. We consider a semiclassically scaled cubic nonlinear…

Mean-field variational methods are widely used for approximate posterior inference in many probabilistic models. In a typical application, mean-field methods approximately compute the posterior with a coordinate-ascent optimization…

Automatic differentiation, as implemented today, does not have a simple mathematical model adapted to the needs of modern machine learning. In this work we articulate the relationships between differentiation of programs as implemented in…

Partial identification approaches are a flexible and robust alternative to standard point-identification approaches in general instrumental variable models. However, this flexibility comes at the cost of a ``curse of cardinality'': the…

In this article we propose a new adaptive numerical quadrature procedure which includes both local subdivision of the integration domain, as well as local variation of the number of quadrature points employed on each subinterval. In this…

We show that nonlinear problems including nonlinear partial differential equations can be efficiently solved by variational quantum computing. We achieve this by utilizing multiple copies of variational quantum states to treat…