Related papers: Compact R-Continuity with Applications to Solving …

We survey elementary results in Minkowski spaces (i.e. finite dimensional Banach spaces) that deserve to be collected together, and give simple proofs for some of them. We place special emphasis on planar results. Many of these results have…

We study properties of continuous semi-homogeneous operators of degree $k$ via various functions (e.g. measures of noncompactness) on all bounded subsets of a Banach space. We prove necessary and sufficient conditions for these functions to…

Motivated by the equivalent definition of a continuous operator between Banach spaces in terms of weakly null nets, we introduce two types of continuous operators between Banach lattices using unbounded absolute weak convergence. We…

There are much recent interests in solving noncovnex min-max optimization problems due to its broad applications in many areas including machine learning, networked resource allocations, and distributed optimization. Perhaps, the most…

This paper introduces a new subtraction operation for convex sets, which defines their difference as a collection of inclusion-minimal convex sets with appropriate definitions of linear operations on them. With these operations the set of…

In this paper we propose a variant of the random coordinate descent method for solving linearly constrained convex optimization problems with composite objective functions. If the smooth part of the objective function has Lipschitz…

This paper extends the theory of rough convergence from normed linear spaces to the more abstract setting of Riesz spaces. We introduce and systematically develop the concept of rough $\mathbb{c}$-convergence ($rc$-convergence) for nets. A…

In mathematical modelling, the data and solutions are represented as measurable functions and their quality is oftentimes captured by the membership to a certain function space. One of the core questions for an analysis of a model is the…

One of the fundamental results of ergodic optimisation asserts that for any dynamical system on a compact metric space $X$ and for any Banach space of continuous real-valued functions on $X$ which embeds densely in $C(X)$ there exists a…

It is well known that in the calculus of variations and in optimization there exist many formulations of the fundamental propositions on the attainment of the infima of sequentially weakly lower semicontinuous coercive functions on…

We demonstrate the necessity of a Poincar\'e type inequality for those metric measure spaces that satisfy Cheeger's generalization of Rademacher's theorem for all Lipschitz functions taking values in a Banach space with the Radon-Nikodym…

Composite optimization offers a powerful modeling tool for a variety of applications and is often numerically solved by means of proximal gradient methods. In this paper, we consider fully nonconvex composite problems under only local…

We initiate the study of nonsmooth optimization problems under bounded local subgradient variation, which postulates bounded difference between (sub)gradients in small local regions around points, in either average or maximum sense. The…

Many problems in nonlinear analysis and optimization, among them variational inequalities and minimization of convex functions, can be reduced to finding zeros (namely, roots) of set-valued operators. Hence numerous algorithms have been…

We prove various notions of uniform continuity for compact-quantum-group representations on Hilbert or Banach spaces equivalent to having finite spectrum, i.e. finitely many isotypic components. This generalizes the classical analogue for…

This paper provides a self-contained exposition of coorbit spaces associated to integrable group representations and quasi-Banach function spaces, and at the same time extends and simplifies previous work. The main results provide an…

We prove an extrapolation of compactness theorem for operators on Banach function spaces satisfying certain convexity and concavity conditions. In particular, we show that the boundedness of an operator $T$ in the weighted Lebesgue scale…

We research proximinality of $\mu$-sequentially compact sets and $\mu$-compact sets in measurable function spaces. Next we show a correspondence between the Kadec-Klee property for convergence in measure and $\mu$-compactness of the sets in…

Many practical optimization problems lack strong convexity. Fortunately, recent studies have revealed that first-order algorithms also enjoy linear convergences under various weaker regularity conditions. While the relationship among…

We study the generic behavior of the method of successive approximations for set-valued mappings in separable Banach spaces. We consider the case of nonexpansive mappings with convex and compact point images and show that for the typical…