相关论文: Isolated calmness and sharp minima via H\"older gr…
Linear singularly perturbed convection-diffusion problems with characteristic layers are considered in three dimensions. We demonstrate the sharpness of our recently obtained upper bounds for the associated Green's function and its…
In recent years several classical results in extremal graph theory have been improved in a uniform way and their proofs have been simplified and streamlined. These results include a new Erd\H{o}s-Stone-Bollob\'as theorem, several stability…
In some optimal control problems, complex relationships between states and inputs cannot be easily represented using continuous constraints, necessitating the use of discrete logic instead. This paper presents a method for incorporating…
In this short note we formulate a stabilizer formalism in the language of noncommutative graphs. The classes of noncommutative graphs we consider are obtained via unitary representations of compact groups, and suitably chosen operators on…
We consider the problem of inference in higher-order undirected graphical models with binary labels. We formulate this problem as a binary polynomial optimization problem and propose several linear programming relaxations for it. We compare…
A generalization of differential operators are pseudodifferential operators which are used for reasoning about partial differential equations with variable coefficients. A lot of useful properties about classical pseudodifferential…
The relaxation in the calculus of variation motivates the numerical analysis of a class of degenerate convex minimization problems with non-strictly convex energy densities with some convexity control and two-sided $p$-growth. The…
The present paper contains some investigations about a uniform variant of the notion of metric hemiregularity, the latter being a less explored property obtained by weakening metric regularity. The introduction of such a quantitative…
In this work, we show that for linearly constrained optimization problems the primal-dual hybrid gradient algorithm, analyzed by Chambolle and Pock [3], can be written as an entirely primal algorithm. This allows us to prove convergence of…
The Isolation Lemma of Mulmuley, Vazirani and Vazirani [Combinatorica'87] provides a self-reduction scheme that allows one to assume that a given instance of a problem has a unique solution, provided a solution exists at all. Since its…
We obtain Calder{\'o}n-Zygmund estimates for some degenerate equations of Kolmogorov type with inhomogeneous coefficients. We then derive the well-posedness of the martingale problem associated to related degenerate operators, and therefore…
In this paper we discuss stability properties of various discretizations for axisymmetric systems including the so called cartoon method which was proposed by Alcubierre, Brandt et.al. for the simulation of such systems on Cartesian grids.…
This paper sheds new light on regularity of multifunctions through various characterizations of directional H\"older /Lipschitz metric regularity, which are based on the concepts of slope and coderivative. By using these characterizations,…
The graph continual release model of differential privacy seeks to produce differentially private solutions to graph problems under a stream of edge updates where new private solutions are released after each update. Thus far, previously…
We discuss computational and qualitative aspects of the fractional Plateau and the prescribed fractional mean curvature problems on bounded domains subject to exterior data being a subgraph. We recast these problems in terms of energy…
Extremal graphical models encode the conditional independence structure of multivariate extremes and provide a powerful tool for quantifying the risk of rare events. Prior work on learning these graphs from data has focused on the setting…
We develop new perturbation techniques for conducting convergence analysis of various first-order algorithms for a class of nonsmooth optimization problems. We consider the iteration scheme of an algorithm to construct a perturbed…
An algorithm is proposed, analyzed, and tested experimentally for solving stochastic optimization problems in which the decision variables are constrained to satisfy equations defined by deterministic, smooth, and nonlinear functions. It is…
We develop an intrinsic geometrical setting for higher order constrained field theories. As a main tool we use an appropriate generalization of the classical Skinner-Rusk formalism. Some examples of application are studied, in particular,…
In this thesis we develop a novel framework to study smooth and strongly convex optimization algorithms, both deterministic and stochastic. Focusing on quadratic functions we are able to examine optimization algorithms as a recursive…