We focus on the minimization of regularized objective functions using the popular half-quadratic approach introduced by Geman and Reynolds in 1992. We show that whenever applicable, this approach is equivalent to the very classical gradient linearization approach, known also as the fixed point iteration.

We study Newton’s method and method based on linearization for solving quasi-variational inequalities in a finite-dimensional real vector space. Projection methods were the most studied methods for solving quasi-variational inequalities and they have linear rates of the convergence. In the paper we establish sufficient conditions for the convergence of Newton’s method and method of linearizatio...

Classical compressed sensing (CS) allows us to recover structured signals from far few linear measurements than traditionally prescribed, thereby efficiently decreasing sampling rates. However, if there exist nonlinearities in the measurements, is it still possible to recover sparse or structured signals from the nonlinear measurements? The research of nonlinear CS is devoted to answering this ...

Extended linearization is the process of factoring a nonlinear system into a linear-like structure x = A(x)x + B(x)u which contains state-dependent coefficient (SDC) matrices. An extended linearization control technique is any technique which (a) treats the SDC matrices A(z) and B(x ) as being constant and (b) uses a linear control synthesis method on the linear-like structure to produce a clos...

This paper presents an exact solution method based on a new linearization scheme for the 0-1 Quadratic Knapsack Problem (QKP) which consists of maximizing a quadratic pseudo-Boolean function with non negative coefficients subject to a linear capacity constraint. Contrasting to traditional linearization schemes, our approach only adds one extra variable. We first convert (QKP) into an equivalent...

We consider the recovery of a potential associated with semi-linear wave equation on R n + 1 , ? . show that an unknown ( x t ) ? u m = 0 can be recovered in Hölder stable way from map | ? ? × [ T ] ? ? ? ? ? L 2 This data is equivalent to inner product Dirichlet-to-Neumann measurement function also prove similar stability result for when there noise added boundary data. The method we use const...

This research deals to introduce a new method for generalizing the well-famed Quantitative Feedback Theory (QFT) in granting robustness of Feedback linearization on nonlinear systems. In this new scheme, first applying feedback linearization, with selecting operating points in domain of system parameter's variations, nonlinear systems replaced with linear systems, then robust controller is desi...

The problem of multi-objective robust feedback linearization controller design of nonlinear system with parametric uncertainties is solved in this paper. The main objective of this paper is to propose an optimal technique to design a robust feedback linearization controller with multi-objective genetic algorithm. A nonlinear system is considered as a benchmark and feedback linearization control...

The paper addresses the problem of dynamic feedback linearization of discrete-time nonlinear control systems. Analogously to the continuous-time case, necessary and sufficient conditions for flatness property are obtained and showed to be equivalent to previously known results on feedback linearizability by endogenous dynamic feedback. An example is added to illustrate the results.