Related papers: Convex invertible cones and Nevanlinna-Pick interp…
With this note we bring again into attention a vector dual problem neglected by the contributions who have recently announced the successful healing of the trouble encountered by the classical duals to the classical linear vector…
This paper considers the inversion of ill-posed linear operators. To regularise the problem the solution is enforced to lie in a non-convex subset. Theoretical properties for the stable inversion are derived and an iterative algorithm akin…
We show that a special class of (nonconvex) NMPC problems admits an exact solution by reformulating them as a finite number of convex subproblems, extending previous results to the multi-input case. Our approach is applicable to a special…
We study several aspects concerning slice regular functions mapping the quaternionic open unit ball into itself. We characterize these functions in terms of their Taylor coefficients at the origin and identify them as contractive…
This work provides a complete characterization of the solutions of a linear interpolation problem for vector polynomials. The interpolation problem consists in finding n scalar polynomials such that an equation involving a linear…
If $\fA$ is a unital weak-$*$ closed algebra of multiplication operators on a reproducing kernel Hilbert space which has the property $\bA_1(1)$, then the cyclic invariant subspaces index a Nevanlinna-Pick family of kernels. This yields an…
We present certain existence criteria and parameterisations for an interpolation problem for completely positive maps that take given matrices from a finite set into prescribed matrices. Our approach uses density matrices associated to…
We describe the set of inner functions of finite order in a multi-connected domain, then we consider an optimization formulation of the Pick-Nevanlinna interpolation problem, and we generalize it to Hermite type interpolation.
The fundamental theorem on commutant lifting due to Sarason does not carry over to the setting of the polydisc. This paper presents two classifications of commutant lifting in several variables. The first classification links the lifting…
We establish new analytic and numerical results on a general class of rational operator Nevanlinna functions that arise e.g. in modelling photonic crystals. The capability of these dielectric nano-structured materials to control the flow of…
Nonnegative matrix factorization is the following problem: given a nonnegative input matrix $V$ and a factorization rank $K$, compute two nonnegative matrices, $W$ with $K$ columns and $H$ with $K$ rows, such that $WH$ approximates $V$ as…
The abstract interpolation problem (AIP) in the Schur class was posed V. Katznelson, A. Kheifets and P. Yuditskii in 1987 as an extension of the V.P. Potapov's approach to interpolation problems. In the present paper an analog of the AIP…
In this paper we introduce the concept of matrix-valued $q$-rational functions. In comparison to the classic case we give different characterizations with principal emphasise on realizations and discuss algebraic manipulations. We also…
Nonlinear convex problems arise in various areas of applied mathematics and engineering. Classical techniques such as the relaxed proximal point algorithm (PPA) and the prediction correction (PC) method were proposed for linearly…
The analysis of linear ill-posed problems often is carried out in function spaces using tools from functional analysis. However, the numerical solution of these problems typically is computed by first discretizing the problem and then…
The theory of imprecise Markov chains has achieved significant progress in recent years. Its applicability, however, is still very much limited, due in large part to the lack of efficient computational methods for calculating…
We give a characterization for the existence of a holomorphic interpolant on the unit polydisc $\mathbb{D}^n,$ $n\geq 2,$ for prescribed three-point Pick--Nevanlinna data. One of the key steps is a characterization for the existence of an…
The problem of finding a solution of nonlinear inclusion problems in Banach space is considered in this paper. Using convex optimization techniques introduced by Robinson (Numer. Math., Vol. 19, 1972, pp. 341-347), a robust convergence…
We consider the problem of matrix completion on an $n \times m$ matrix. We introduce the problem of Interpretable Matrix Completion that aims to provide meaningful insights for the low-rank matrix using side information. We show that the…
Conventional inverse optimization inputs a solution and finds the parameters of an optimization model that render a given solution optimal. The literature mostly focuses on inferring the objective function in linear problems when accepted…