This paper introduces new methods of identification and estimation the first-price sealed bid auction model compares them with previous existing ones. The first method allows us to estimate directly (through an iterative algorithm) cumulative distribution function private values without estimating beforehand. In second method, we use a quantile approach. Although is complex nonlinear inverse pr...

Inexact Newton regularization methods have been proposed by Hanke and Rieder for solving nonlinear ill-posed inverse problems. Every such a method consists of two components: an outer Newton iteration and an inner scheme providing increments by regularizing local linearized equations. The method is terminated by a discrepancy principle. In this paper we consider the inexact Newton regularizatio...

Recently, a considerable growth of interest in projected gradient (PG) methods has been observed due to their high efficiency in solving large-scale convex minimization problems subject to linear constraints. Since the minimization problems underlying nonnegative matrix factorization (NMF) of large matrices well matches this class of minimization problems, we investigate and test some recent PG...

In this paper we discuss the construction, analysis, and implementation of iterative schemes for the solution of inverse problems based on total variation regularization. Via different approximations of the nonlinearity we derive three different schemes resembling three well-known methods for nonlinear inverse problems in Hilbert spaces, namely iterated Tikhonov, Levenberg-Marquardt, and Landwe...

A strong connection is established between the structural and the looking back techniques for manipulating the relative complexity of computable functions and exploring the nature of subrecursive reducibilities. Looking back serves as a basis for a simple and general structural result which can be used to derive many fundamental properties of subrecursive degrees and complexity classes. For exa...

We provide fast and accurate adaptive algorithms for the spatial resolution of current densities in MEG. We assume that vector components of the current densities possess a sparse expansion with respect to preassigned wavelets. Additionally, different components may also exhibit common sparsity patterns. We model MEG as an inverse problem with joint sparsity constraints, promoting coupling of n...

In our papers [Inverse Problems, 15, 309-327,1999] and [Numer. Math., 88, 347-365, 2001] we proposed algorithm REGINN being an inexact Newton iteration for the stable solution of nonlinear ill-posed problems. REGINN consists of two components: the outer iteration, which is a Newton iteration stopped by the discrepancy principle, and an inner iteration, which computes the Newton correction by so...

Abstract We consider abstract inverse problems between infinite-dimensional Banach spaces. These are typically nonlinear and ill-posed, making the inversion with limited noisy measurements a delicate process. In this work, we assume that unknown belongs to finite-dimensional manifold: assumption arises in many real-world scenarios where natural objects have low intrinsic dimension belong certai...