Related papers: Higher-Order Metric Subregularity and Its Applicat…
The aim of this paper is to give not only an explicit upper bound of the total Q-curvature but also an induced isoperimetric deficit formula for the complete conformal metrics on $\mathbb R^n$, $n\ge 3$ with scalar curvature being…
In this paper, we propose new linearly convergent second-order methods for minimizing convex quartic polynomials. This framework is applied for designing optimization schemes, which can solve general convex problems satisfying a new…
Because the distant retrograde orbits dynamics inherently depends on special functions, approximate analytical solutions in the literature are commonly constrained to providing rough approximations of the qualitative behavior. We rely on…
Most uncertainty quantification (UQ) approaches provide a single scalar value as a measure of model reliability. However, different uncertainty measures could provide complementary information on the prediction confidence. Even measures…
We provide a generalization of first-order necessary conditions of optimality for infinite-dimensional optimization problems with a finite number of inequality constraints and with a finite number of inequality and equality constraints. Our…
The paper is briefly dealing with greater or lesser misused normalization in self-modeling/multivariate curve resolution (S/MCR) practice. The importance of the correct use of the ode solvers and apt kinetic illustrations are elucidated.…
The study of first-order optimization algorithms (FOA) typically starts with assumptions on the objective functions, most commonly smoothness and strong convexity. These metrics are used to tune the hyperparameters of FOA. We introduce a…
We introduce the notion of dynamical metric order of a continuous map on a compact metric space, study its basic properties, and compute it for several classes of maps. This concept which is a counterpart of the metric mean dimension with…
In this paper, we address the problem of prescribing non-constant $Q$ and boundary $T$ curvatures on the upper hemisphere $\mathbb{S}^4_+\subset \mathbb{R}^5$, via a conformal change of the background metric. This is equivalent to solve a…
In this paper a special semi-smooth equation associated to the second order cone is studied. It is shown that, under mild assumptions, the semi-smooth Newton method applied to this equation is well-defined and the generated sequence is…
This paper investigates strong metric subregularity around a reference point as introduced by H. Gfrerer and J. V. Outrata. In the setting of Banach spaces, we analyse its stability under Lipschitz continuous perturbations and establish its…
Some concepts, such as non-compactness measure and condensing operators, defined on metric spaces are extended to uniform spaces. Such extensions allow us to locate, in the context of uniform spaces, some classical results existing in…
Nonlinear parametric inverse problems appear in many applications and are typically very expensive to solve, especially if they involve many measurements. These problems pose huge computational challenges as evaluating the objective…
The paper is mainly devoted to systematic developments and applications of geometric aspects of second-order variational analysis that are revolved around the concept of parabolic regularity of sets. This concept has been known in…
We investigate the behavior of the solutions of a class of certain strictly hyperbolic equations defined on $[0,T]\times \R^n$ in relation to a class of metrics on the phase space. In particular, we study the global regularity and decay…
Supersymmetric and parasupersymmetric quantum mechanics are now recognized as two further parts of quantum mechanics containing a lot of new informations enlightening (solvable) physical applications. Both contents are here analysed in…
Inverse problems arise in a number of domains such as medical imaging, remote sensing, and many more, relying on the use of advanced signal and image processing approaches -- such as sparsity-driven techniques -- to determine their…
In these notes we explore a variety of models comprising a large number of constituents. An emphasis is placed on integrals over large Hermitian matrices, as well as quantum mechanical models whose degrees of freedom are organised in a…
Higher order conformal perturbation theory is studied for theories with and without boundaries. We identify systematically the universal quantities in the beta function equations, and we give explicit formulae for the universal coefficients…
In this paper, we show a series of abstract results on fixed point regularity with respect to a parameter. They are based on a Taylor development taking into account a loss of regularity phenomenon, typically occurring for composition…