Related papers: Linear Monotone Subspaces of Locally Convex Spaces
The property of isotonicity of a continuous convex function defined on the entire space or only on the positive cone is characterized via subdifferentials. Numerous examples illustrating the obtained results are included.
Identifying locally optimal solutions is an important issue given an optimization model. In this paper, we focus on a special class of symmetric tensors termed regular simplex tensors, which is a newly-emerging concept, and investigate its…
The paper is devoted to the problem of exact calculation of the norms in ideal spaces for monotone operators on the cones of functions with monotonicity properties. We implement a general approach to this problem that covers many concrete…
A characterization of valuations on the space of convex Lipschitz functions whose domain is a polytope in $\mathbb{R}^n$ is obtained. It is shown that every upper semicontinuous, equi-affine and dually epi-translation invariant valuation…
The purpose of this paper is to systematically study compactness and essential norm properties of operators on a very general class of weighted Fock spaces over $\C$. In particular, we obtain rather strong necessary and sufficient…
We discuss the concept of invariant subspaces for unbounded linear operators, point out some shortcomings of known definitions, and propose our own.
Functions with uniform sublevel sets can represent orders, preference relations or other binary relations and thus turn out to be a tool for scalarization that can be used in multicriteria optimization, decision theory, mathematical…
Monotone systems constitute one of the most important classes of dynamical systems used in mathematical biology modeling. The objective of this paper is to extend the notion of monotonicity to systems with inputs and outputs, a necessary…
We characterize the extreme points of multidimensional monotone functions from $[0,1]^n$ to $[0,1]$, as well as the extreme points of the set of one-dimensional marginals of these functions. These characterizations lead to new results for…
We consider rather a general class of multi-level optimization problems, where a convex objective function is to be minimized subject to constraints of optimality of nested convex optimization problems. As a special case, we consider a…
In the first part of the note we prove that a sufficient condition (due to Simons) for the convexity of the closure of the domain/range of a monotone operator is also necessary when the operator has bounded domain and is maximal. Simons'…
We use the method of monotone iterations to obtain fixed point and coupled fixed point results for mixed monotone operators in the setting of partially ordered sets, with no additional assumptions on the partial order and with no…
In this note, we study maximal monotonicity of linear relations (set-valued operators with linear graphs) on reflexive Banach spaces. We provide a new and simpler proof of a result due to Brezis-Browder which states that a monotone linear…
MINLO (mixed-integer nonlinear optimization) formulations of the disjunction between the origin and a polytope via a binary indicator variable have broad applicability in nonlinear combinatorial optimization, for modeling a fixed cost $c$…
This paper is about certain linear subspaces of Banach SN spaces (that is to say Banach spaces which have a symmetric nonexpansive linear map into their dual spaces). We apply our results to monotone linear subspaces of the product of a…
We give an iteration scheme for finding zeros of maximal monotone operators in Hilbert spaces. We assume that the operator is defined in the whole space. The iterates converge strongly to a solution if there exists any, otherwise they tend…
We develop a holomorphic functional calculus for (multivalued linear) operators on locally convex vector spaces. This includes the case of fractional powers along Lipschitz curves.
Fitzpatrick's variational representation of maximal monotone operators is here extended to a class of pseudo-monotone operators in Banach spaces. On this basis, the initial-value problem associated with the first-order flow of such an…
Current work on human-machine alignment aims at understanding machine-learned latent spaces and their correspondence to human representations. G{\"a}rdenfors' conceptual spaces is a prominent framework for understanding human…
In this paper, the main aim is to consider the boundedness of commutators of multilinear Calder\'{o}n-Zygmund operators with Lipschitz functions in the context of the variable exponent Lebesgue spaces. Furthermore, the variable versions of…