Abstract We analyze dynamical properties of the logarithmic Schrödinger equation under a quadratic potential. The sign nonlinearity is such that it known in absence external potential, every solution dispersive, with universal asymptotic profile. introduction harmonic potential generates solitary waves, corresponding to generalized Gaussons. prove they are orbitally stable, using an inequality ...

Nonlinear rescaling (NR) methods alternate finding an unconstrained minimizer of the Lagrangian for the equivalent problem in the primal space (which is an infinite procedure) with Lagrange multipliers update. We introduce and study a proximal point nonlinear rescaling (PPNR) method that preserves convergence and retains a linear convergence rate of the original NR method and at the same time d...

We propose a primal-dual continuation approach for the capacitated multifacilityWeber problem (CMFWP) based on its nonlinear second-order cone program (SOCP) reformulation. The main idea of the approach is to reformulate the CMFWP as a nonlinear SOCP with a nonconvex objective function, and then introduce a logarithmic barrier term and a quadratic proximal term into the objective to construct a...

Achievable rate distortion region for the quadratic Gaussian multi-terminal source coding was recently solved by Wagner, Tavildar, and Viswanath [1]. Although it is a very important result, the proofs are somewhat ad-hoc and hard to be generalized. Recently, Courtade and Weissman [2] established the complete achievable rate region of two-encoder multi-terminal source coding problem under logari...

Abstract This paper introduces QPDO, a primal-dual method for convex quadratic programs which builds upon and weaves together the proximal point algorithm damped semismooth Newton method. The outer regularization yields numerically stable method, we interpret operator as unconstrained minimization of augmented Lagrangian function. allows inner scheme to exploit sparse symmetric linear solvers m...

We introduce a new barrier function which has a linear growth term in its kernel function. So far all existing kernel functions have a quadratic (or higher degree) growth term. Despite this, a large-update primal-dual interior-point method based on this kernel function has the same iteration bound as the classical primal-dual method, which is based on the logarithmic barrier method.

It has recently been shown that the logarithmic barrier method for solving nite-dimensional, linearly constrained quadratic optimization problems can be extended to an innnite-dimensional setting with complexity estimates similar to the nite dimensional case. As a consequence, an eecient computational method for solving the linearly constrained LQ control problem is now a vailable. In this pape...

Psi-series (i.e., logarithmic series) of quadratic systems on the plane are considered. Its existence and convergence is studied, and an algorithm of location of logarithmic singularities is developed. Moreover, the relationship between psi-series and non-integrability is stressed and in particular it is proved that quadratic systems with psi-series that are not Laurent series do not have an al...

In this paper we discuss the importance sampling Monte Carlo methods for pricing options. The classical importance sampling method is used to eliminate the variance caused by the linear part of the logarithmic function of payoff. The variance caused by the quadratic part is reduced by stratified sampling. We eliminate both kinds of variances just by importance sampling. The corresponding space ...