Related papers: General monotonicity
This work deals with the generation of theoretical correlation matrices with specific sparsity patterns, associated to graph structures. We present a novel approach based on convex optimization, offering greater flexibility compared to…
Manifold optimization is ubiquitous in computational and applied mathematics, statistics, engineering, machine learning, physics, chemistry and etc. One of the main challenges usually is the non-convexity of the manifold constraints. By…
In the paper, the authors review origins, motivations, and generalizations of a series of inequalities involving several exponential functions and sums, establish three new inequalities involving finite exponential functions and sums by…
In this paper we study local unitary invariants of a multi-partite quantum state that are monotonic, on average, under local operations and classical communication (locc). In particular we focus on local unitary invariants that are…
The purpose of this paper is to prove the existence of solutions of quasi-equilibrium problems without any generalized monotonicity assumption. Additionally, we give an application to quasi-optimization problems.
We introduce a new class of convex-regularized Optimal Transport losses, which generalizes the classical Entropy-regularization of Optimal Transport and Sinkhorn divergences, and propose a generalized Sinkhorn algorithm. Our framework…
We consider a class of combinatorial optimization problems that emerge in a variety of domains among which: condensed matter physics, theory of financial risks, error correcting codes in information transmissions, molecular and protein…
In this paper, we introduce methods from convex optimization to solve the multimarginal transport type problems arise in the context of density functional theory. Convex relaxations are used to provide outer approximation to the set of…
In this expository article, we discuss various monotonicity formulas for parabolic and elliptic operators and explain how the analysis of the function spaces and the geometry of the underlining spaces are intertwined. After briefly…
Inspired by a recent result of Funano's, we provide a sharp quantitative comparison result between the first nontrivial eigenvalues of the Neumann Laplacian on bounded convex domains $\Omega_{1} \subset \Omega_{2}$ in any dimension $d$…
We study a specific convex maximization problem in n-dimensional space. The conjectured solution is proved to be a vertex of the polyhedral feasible region, but only a partial proof of local maximality is known. Integer sequences with…
Using the Markov distance and Ptolemy inequality introduced by Lee-Li-Rabideau-Schiffler \cite{LLRS}, we completely determine the monotonicity of the generalized Markov numbers along the lines of a given slope.
We focus on the solutions of second-order stable linear difference equations and demonstrate that their behavior can be non-monotone and exhibit peak effects depending on initial conditions. The results are applied to the analysis of the…
For many real-life Bayesian networks, common knowledge dictates that the output established for the main variable of interest increases with higher values for the observable variables. We define two concepts of monotonicity to capture this…
Consider a sum of convex functions, where the only information known about each individual summand is the location of a minimizer. In this work, we give an exact characterization of the set of possible minimizers of the sum. Our results…
We construct a version of kneading theory for families of monotonous functions on the real line. The generality of the setup covers two classical results from Milnor-Thurston's kneading theory: the first one is to dynamically characterise…
In many practical applications, heuristic or approximation algorithms are used to efficiently solve the task at hand. However their solutions frequently do not satisfy natural monotonicity properties of optimal solutions. In this work we…
We analyse the relationship between the full additivity of the entanglement cost and its full monotonicity under local operations and classical communication. We show that the two properties are equivalent for the entanglement cost. The…
Generalized entropic projections and dominating points are solutions to convex minimization problems related to conditional laws of large numbers. They appear in many areas of applied mathematics such as statistical physics, information…
In this work we deal with the so-called path convexities, defined over special collections of paths. For example, the collection of the shortest paths in a graph is associated with the well-known geodesic convexity, while the collection of…