Related papers: Minimization of convex functionals over frame oper…
We study the spectral properties of positive absolutely minimum attaining operators defined on infinite dimensional complex Hilbert spaces and using that derive a characterization theorem for such type of operators. We construct several…
In this work, operator version of Popoviciu's inequality for positive selfadjoint operators in Hilbert spaces under positive linear maps for superquadratic functions is proved. Analogously, using the same technique operator version of…
One revisits the standard saddle-point method based on conjugate duality for solving convex minimization problems. Our aim is to reduce or remove unnecessary topological restrictions on the constraint set. Dual equalities and…
Detecting hidden convexity is one of the tools to address nonconvex minimization problems. After giving a formal definition of hidden convexity, we introduce the notion of conditional infimum, as it will prove instrumental in detecting…
The classical frame potential in a finite dimensional Hilbert space has been introduced by Benedetto and Fickus, who showed that all finite unit-norm tight frames can be characterized as the minimizers of this energy functional. This was…
The problem of minimizing convex functionals of probability distributions is solved under the assumption that the density of every distribution is bounded from above and below. A system of sufficient and necessary first-order optimality…
Finite frames, or spanning sets for finite-dimensional Hilbert spaces, are a ubiquitous tool in signal processing. There has been much recent work on understanding the global structure of collections of finite frames with prescribed…
Set-functions appear in many areas of computer science and applied mathematics, such as machine learning, computer vision, operations research or electrical networks. Among these set-functions, submodular functions play an important role,…
A polyhedral convex set optimization problem is given by a set-valued objective mapping from the $n$-dimensional to the $q$-dimensional Euclidean space whose graph is a convex polyhedron. This problem can be seen as the most elementary…
In this paper, we introduce and study frame of operators in quaternionic Hilbert spaces as a generalization of g frames which in turn generalized various notions like Pseduo frames, bounded quasi-projectors and frame of subspaces (fusion…
We investigate the asymptotic behavior of sequences generated by the proximal point algorithm for convex functions in complete geodesic spaces with curvature bounded above. Using the notion of resolvents of such functions, which was…
We consider frames F in a given Hilbert space, and we show that every F may be obtained in a constructive way from a reproducing kernel and an orthonormal basis in an ambient Hilbert space. The construction is operator-theoretic, building…
In this paper, we investigate the concept of p-convexity for sets and functions in n-dimensional Euclidean space. We establish novel algebraic and topological results within this generalized convexity framework. Furthermore, we analyze…
To a generalized tight continuous frame in a Hilbert space $\H$ indexed by a locally compact space $\Si$ endowed with a Radon measure, one associates a coorbit theory converting spaces of functions on $\Si$ in spaces of vectors comparable…
This paper studies simple bilevel problems, where a convex upper-level function is minimized over the optimal solutions of a convex lower-level problem. We first show the fundamental difficulty of simple bilevel problems, that the…
This paper investigates first-order variable metric backward forward dynamical systems associated with monotone inclusion and convex minimization problems in real Hilbert space. The operators are chosen so that the backward-forward…
The geometric problem of estimating an unknown compact convex set from evaluations of its support function arises in a range of scientific and engineering applications. Traditional approaches typically rely on estimators that minimize the…
In this work we solve, for given bounded operators $B,C$ and Hilbert-Schmidt operator $M$ acting on potentially infinite-dimensional separable Hilbert spaces, the reduced rank approximation problem, $\min\{\lVert M-BXC\rVert_{L_2}:\…
The local boundedness of classes of operators is analyzed on different subsets directly related to their Fitzpatrick functions and characterizations of the topological vector spaces for which that local boundedness holds is given in terms…
Operator convex functions defined on the positive half-line play a prominent role in the theory of quantum information, where they are used to define quantum $f$-divergences. Such functions admit integral representations in terms of…