Related papers: Extremum Problems with Total Variation Distance an…
We consider an inverse problem for the linear one-dimensional wave equation with variable coefficients consisting in determining an unknown source term from a boundary observation. A method to obtain approximations of this inverse problem…
The paper is concerned with a class of nonlinear free boundary problems, which are usually solved by variational methods based on primal (or primal-dual) variational settings. We deduce and investigate special relations (error identities).…
This paper investigates the use of extreme value theory for modelling the distribution of demand-net-of-wind for capacity adequacy assessment. Extreme value theory approaches are well-established and mathematically justified methods for…
Let $S$ be a Polish space and $(X_n:n\geq1)$ an exchangeable sequence of $S$-valued random variables. Let $\alpha_n(\cdot)=P(X_{n+1}\in \cdot\mid X_1,\...,X_n)$ be the predictive measure and $\alpha$ a random probability measure on $S$ such…
From environmental sciences to finance, there is a growing demand for methods that can assess the risks of extreme events beyond those observed in available data. Extrapolating extreme events beyond the range of the data is not obvious.…
We develop an interpolation-based modeling framework for parameter-dependent partial differential equations arising in control, inverse problems, and uncertainty quantification. The solution is discretized in the physical domain using…
We give solutions to some extremal problems involving distance function in mixed norm spaces of harmonic functions on the unit ball of R^n
This paper investigates multivariable extremum seeking using unit-vector control. By employing the gradient algorithm and a polytopic embedding of the unknown Hessian matrix, we establish sufficient conditions, expressed as linear matrix…
This paper is devoted to variational problems on the set of probability measures which involve optimal transport between unequal dimensional spaces. In particular, we study the minimization of a functional consisting of the sum of a term…
The task of estimating a matrix given a sample of observed entries is known as the \emph{matrix completion problem}. Most works on matrix completion have focused on recovering an unknown real-valued low-rank matrix from a random sample of…
In this paper we develop new extremal principles in variational analysis that deal with finite and infinite systems of convex and nonconvex sets. The results obtained, unified under the name of tangential extremal principles, combine primal…
Entropy is a measure of heterogeneity widely used in applied sciences, often when data are collected over space. Recently, a number of approaches has been proposed to include spatial information in entropy. The aim of entropy is to…
A multidimensional extremal problem in the idempotent algebra setting is considered which consists in minimizing a nonlinear functional defined on a finite-dimensional semimodule over an idempotent semifield. The problem integrates two…
We present and study approximate notions of dimensional and margin complexity, which correspond to the minimal dimension or norm of an embedding required to approximate, rather then exactly represent, a given hypothesis class. We show that…
In this paper we introduce new notions of local extremality for finite and infinite systems of closed sets and establish the corresponding extremal principles for them called here rated extremal principles. These developments are in the…
A fundamental challenge in probabilistic modeling is to balance expressivity and inference efficiency. Tractable probabilistic models (TPMs) aim to directly address this tradeoff by imposing constraints that guarantee efficient inference of…
We look for pointwise bounds on a plurisubharmonic function near its singularity point, given the value of its generalized Lelong number with respect to a plurisubharmonic weight. To this end, an extremal problem is considered. In certain…
A pivotal problem in Bayesian nonparametrics is the construction of prior distributions on the space M(V) of probability measures on a given domain V. In principle, such distributions on the infinite-dimensional space M(V) can be…
Among many topological indices of trees the sum of distances $\sigma(T)$ and the number of subtrees $F(T)$ have been a long standing pair of graph invariants that are well known for their negative correlation. That is, among various given…
We introduce a new class of extremum seeking controllers able to achieve fixed time convergence to the solution of optimization problems defined by static and dynamical systems. Unlike existing approaches in the literature, the convergence…