This article concernes the method of approximate inverse to solve semi-discrete, linear operator equations in Banach spaces. Semi-discrete means that we search a solution in an infinite dimensional Banach space having only a finite number of data available. In this sense the situation is applicalble to a large variety of applications where a measurement process delivers a discretization of an i...

The novel concept of total generalized variation of a function u is introduced and some of its essential properties are proved. Differently from the bounded variation semi-norm, the new concept involves higher order derivatives of u. Numerical examples illustrate the high quality of this functional as a regularization term for mathematical imaging problems. In particular this functional selecti...

An algebraic formulation of general relativity is proposed. The formulation is applicable to quantum gravity and noncommutative space. To investigate quantum gravity we develop the canonical formalism of operator geometry, after reconstructing an algebraic canonical formulation on analytical dynamics. The remarkable fact is that the constraint equation of the gravitational system is algebraical...

Portfolio optimization problems on a finite time horizon under proportional transaction costs are considered. The objective is to maximize the expected utility of the terminal wealth. The ensuing non-smooth timedependent Hamilton-Jacobi-Bellman (HJB) equation is solved by regularization and the application of a semi-smooth Newton method. Discretization in space is carried out by finite differen...

We propose a partial differential equation to be used for interpolating M -channel data, such as digital color images. This equation is derived via a semi-group from a variational regularization method for minimizing displacement errors. For actual image interpolation, the solution of the PDE is projected onto a space of functions satisfying interpolation constraints. A comparison of the test r...

Abstract. Optimal control problems with convex but non-smooth cost functional are considered. The non-smoothness arises from a L-norm in the objective functional, which recently attracted much research effort in the context of inverse problems. The problem is regularized to permit the use of semi-smooth Newton method. Error estimates with respect to the regularization parameter are provided. Mo...

In this paper, we consider a class of fuzzy implicit variational inequalities with linear membership functions. By using the “tolerance approach”, we show that solving such problems can be reduced to a semi-infinite programming problem. A version of the “method of centres” with “entropic regularization” techniques, only used a quasi-Newton line search using MATLAB software is required in our im...

The problem of constructing classification methods based on both classified and unclassified data sets is considered for analyzing data with complex structures. We introduce a semi-supervised logistic discriminant model with Gaussian basis expansions. Unknown parameters included in the logistic model are estimated by regularization method along with the technique of EM algorithm. For selection ...

in this letter we have proposed a new regularization scheme to deal with the divergent integralsoccurring in the quantum mechanical problem of calculating the bound state energy of the delta-functionpotential in two and three dimensions. based on the schwinger parameterization technique we argue thatthere are no infinities even in d dimensions. in this way we were able to compare our proposal w...

Graph smoothness objectives have achieved great success in semi-supervised learning but have not yet been applied extensively to unsupervised generative models. We define a new class of entropic graph-based posterior regularizers that augment a probabilistic model by encouraging pairs of nearby variables in a regularization graph to have similar posterior distributions. We present a three-way a...