Related papers: Strong Duality Theorem for Continuous-Time Linear …
We consider estimation of parameters defined as linear functionals of solutions to linear inverse problems. Any such parameter admits a doubly robust representation that depends on the solution to a dual linear inverse problem, where the…
In answer set programming, two groups of rules are considered strongly equivalent if they have the same meaning in any context. Strong equivalence of two programs can be sometimes established by deriving rules of each program from rules of…
This paper is a study of first-order coherent logic from the point of view of duality and categorical logic. We prove a duality theorem between coherent hyperdoctrines and open polyadic Priestley spaces, which we subsequently apply to prove…
In this paper, we prove the strong Feller property for stochastic delay (or functional) differential equations with singular drift. We extend an approach of Maslowski and Seidler to derive the strong Feller property of those equations. The…
The theory of monotonicity and duality is developed for general one-dimensional Feller processes. Moreover it is shown that local monotonicity conditions (conditions on the L\'evy kernel) are sufficient to prove the well-posedness of the…
In the vicinity of a solution of a nonlinear programming problem at which both strict complementarity and linear independence of the active constraints may fail to hold, we describe a technique for distinguishing weakly active from strongly…
We propose an algorithm-independent framework to equip existing optimization methods with primal-dual certificates. Such certificates and corresponding rate of convergence guarantees are important for practitioners to diagnose progress, in…
We introduce the framework of qualitative optimization problems (or, simply, optimization problems) to represent preference theories. The formalism uses separate modules to describe the space of outcomes to be compared (the generator) and…
We study a fine hierarchy of Borel-piecewise continuous functions, especially, between closed-piecewise continuity and $G_\delta$-piecewise continuity. Our aim is to understand how a priority argument in computability theory is connected to…
By time discretization of a second-order primal-dual dynamical system with damping $\alpha/t$ where an inertial construction in the sense of Nesterov is needed only for the primal variable, we propose a fast primal-dual algorithm for a…
We give a short, self-contained, and elementary proof of the strong law of large numbers under a power law decay hypothesis for joint second moments. The result is related to the classical one by Lyons. However, we also provide a rate of…
In this note, we study the relation between Fontaine-Laffaille modules and strongly divisible modules, without assuming the main theorem of Fontaine-Laffaille (but we need to assume the main results concerning strongly divisible modules).…
The completeness of the group classification of systems of two linear second-order ordinary differential equations with constant coefficients is delineated in the paper. The new cases extend what has been done in the literature. These cases…
We consider a primal-dual algorithm for minimizing $f(x)+h\square l(Ax)$ with Fr\'echet differentiable $f$ and $l^*$. This primal-dual algorithm has two names in literature: Primal-Dual Fixed-Point algorithm based on the Proximity Operator…
The paper addresses a continuous-time continuous-space chance-constrained stochastic optimal control (SOC) problem where the probability of failure to satisfy given state constraints is explicitly bounded. We leverage the notion of exit…
Linear Programs (LP) are celebrated widely, particularly so in machine learning where they have allowed for effectively solving probabilistic inference tasks or imposing structure on end-to-end learning systems. Their potential might seem…
This article fits in the area of research that investigates the application of topological duality methods to problems that appear in theoretical computer science. One of the eventual goals of this approach is to derive results in…
A recent line of research investigates how algorithms can be augmented with machine-learned predictions to overcome worst case lower bounds. This area has revealed interesting algorithmic insights into problems, with particular success in…
For many common height functions, it is notoriously hard to compute the essential minimum. Nevertheless there are two classical methods, one giving lower bounds and the other giving upper bounds. In this paper, we show that the two methods…
Disjunctive finitary programs are a class of logic programs admitting function symbols and hence infinite domains. They have very good computational properties, for example ground queries are decidable while in the general case the stable…