Related papers: Aubin Property and Strong Regularity Are Equivalen…

Unconstrained binary integer programming (UBIP) poses significant computational challenges due to its discrete nature. We introduce a novel reformulation approach using a piecewise cubic function that transforms binary constraints into…

This work introduces a new cubic regularization method for nonconvex unconstrained multiobjective optimization problems. At each iteration of the method, a model associated with the cubic regularization of each component of the objective…

Let $n\ge2$, $\Omega\subset\mathbb{R}^n$ be a bounded one-sided chord arc domain, and $p\in(1,\infty)$. In this article, we study the (weak) $L^p$ Poisson--Robin(-regularity) problem for a uniformly elliptic operator…

We develop a new method for equality constrained optimization problems based on a sequential cubic programming framework. Each iteration utilizes a step decomposition based on the Jacobian of the constraints into a normal and a tangential…

We extend the standard notion of self-concordance to non-convex optimization and develop a family of second-order algorithms with global convergence guarantees. In particular, two function classes -- \textit{weakly self-concordant}…

We study the problem of stopping a Brownian motion at a given distribution $\nu$ while optimizing a reward function that depends on the (possibly randomized) stopping time and the Brownian motion. Our first result establishes that the set…

We consider non-autonomous wave equations \[ \left\{ \begin{aligned} \&\ddot u(t) + \B(t)\dot u(t) + \A(t)u(t) = f(t) \quad t\text{-a.e.}\\ \&u(0)=u_0,\, \dot u(0) = u_1. \end{aligned} \right. \] where the operators $\A(t)$ and $\B(t)$ are…

We concerns here with the continuity on the geometry of the second Riemannian L^p-Sobolev best constant B_0(p,g) associated to the AB program. Precisely, for 1 <= p <= 2, we prove that B_0(p,g) depends continuously on g in the C^2-topology.…

Many nonlinear optimal control and optimization problems involve constraints that combine continuous dynamics with discrete logic conditions. Standard approaches typically rely on mixed-integer programming, which introduces scalability…

In this note, we study the complex constant rank condition for differential operators and its implications for coercive differential inequalities. These are inequalities of the form \[ \Vert A u \Vert_{L^p} \leq \Vert \mathscr{A} u…

In this paper we study the local regularity properties of weak solutions to a special class of anisotropic doubly nonlinear parabolic operators, whose prototype is the anisotropic Trudinger's equation $$ u_t- \sum\limits_{i=1}^N…

Robustness is a correctness notion for concurrent programs running under relaxed consistency models. The task is to check that the relaxed behavior coincides (up to traces) with sequential consistency (SC). Although computationally simple…

We consider the problem of deciding $\omega$-regular properties on infinite traces produced by linear loops. Here we think of a given loop as producing a single infinite trace that encodes information about the signs of program variables at…

In this paper, we readdress the classical topic of second-order sufficient optimality conditions for optimization problems with nonsmooth structure. Based on the so-called second subderivative of the objective function and of the indicator…

We consider a boundary value problem for a general second order linear equation in a domain with a fine perforation. The latter is made by small cavities; both the shapes of the cavities and their distribution are arbitrary. The boundaries…

The problem of optimizing over random structures emerges in many areas of science and engineering, ranging from statistical physics to machine learning and artificial intelligence. For many such structures finding optimal solutions by means…

In this paper we establish well posedness of the Neumann problem with boundary data in $L^2$ or the Sobolev space $\dot W^2_{-1}$, in the half space, for linear elliptic differential operators with coefficients that are constant in the…

We study property testing in the subcube conditional model introduced by Bhattacharyya and Chakraborty (2017). We obtain the first equivalence test for $n$-dimensional distributions that is quasi-linear in $n$, improving the previously…

Logic programming under the answer-set semantics nowadays deals with numerous different notions of program equivalence. This is due to the fact that equivalence for substitution (known as strong equivalence) and ordinary equivalence are…

We consider the cubic nonlinear Schr\"odinger equation with a spatially rough potential, a key equation in the mathematical setup for nonlinear Anderson localization. Our study comprises two main parts: new optimal results on the…