In this paper, we study the power allocation problem for a cognitive radio in the presence of a smart jammer over parallel Gaussian channels. The objective of the jammer is to minimize the total capacity achievable by the cognitive radio. We model the interaction between the two players as a zero-sum game, for which we derive the saddle point closed form expression. First, we start by solving e...

In the last decade, the problems related to l1/nuclear norm minimization attract a lot of attention in Signal Processing, Machine Learning and Optimization communities. In this paper, devoted to `1/nuclear norm minimization as “optimization beasts,” we give a detailed description of two attractive First Order optimization techniques for solving the problems of this type. The first one, aimed pr...

We study H(div) preconditioning for the saddle-point systems that arise in a stochastic Galerkin mixed formulation of the steady-state diffusion problem with random data. The key ingredient is a multigrid V-cycle for a weighted, stochastic H(div) operator, acting on a certain tensor product space of random fields with finite variance. We build on the Arnold-Falk-Winther multigrid algorithm pres...

We consider the numerical simulation of an optimal control problem constrained by the unsteady Stokes-Brinkman equation involving random data. More precisely, we treat the state, the control, the target (or the desired state), as well as the viscosity, as analytic functions depending on uncertain parameters. This allows for a simultaneous generalized polynomial chaos approximation of these rand...

We consider a generic convex-concave saddle point problem with a separable structure, a form that covers a wide-ranged machine learning applications. Under this problem structure, we follow the framework of primal-dual updates for saddle point problems, and incorporate stochastic block coordinate descent with adaptive stepsizes into this framework. We theoretically show that our proposal of ada...

We compute the full three-dimensional momentum space distribution of ejected electrons resulting from alpha particle impact ionization of hydrogen. At low impact velocities the transverse momentum distributions are shown to exhibit strong oscillations with energy. For the longitudinal component, the momentum distribution peaks near the target at high energies, shifts towards the projectile cent...

In this paper, we present an inexact primal–dual method with correction step for a saddle point problem by introducing the notations of extended proximal operators symmetric positive definite matrix D. Relaxing requirement on sizes, prove convergence proposed method. We also establish O(1/N) rate our in ergodic sense. Moreover, apply to solve TV- $$\hbox {L}_1$$ image deblurring problems. Numer...

This paper is devoted to the analysis of the eigenvalue distribution of two classes of block preconditioners for the generalized saddle point problem. Most of the bounds developed improve those appeared in previously published works. Numerical results onto a realistic test problem give evidence of the effectiveness of the estimates on the spectrum of preconditioned matrices. Copyright © 2011 Jo...

After a brief introduction to the spectral analysis of saddle point matrices, in this talk we present new estimates for the eigenvalue intervals for symmetric saddle-point and regularised saddle-point matrices in the case where the (1,1) block may be indefinite. These generalise known results for the definite (1,1) case. We also discuss spectral properties of the equivalent augmented formulatio...