Related papers: Conditional Analysis on R^d

Let $(R,\mathfrak{m})$ be a Noetherian local ring and $\widehat{R}$ its $\mathfrak{m}$-adic completion. We study the problem of determining when a finitely generated $\widehat{R}$-module arises from an $R$-module, i.e., when it is…

Concerning bivariate least squares linear regression, the classical approach pursued for functional models in earlier attempts is reviewed using a new formalism in terms of deviation (matrix) traces. Within the framework of classical error…

We propose two novel conditional gradient-based methods for solving structured stochastic convex optimization problems with a large number of linear constraints. Instances of this template naturally arise from SDP-relaxations of…

We look for the minimizers of the functional $\jla{\la}(\oo)=\la|\oo|-P(\oo)$ among planar convex domains constrained to lie into a given ring. We prove that, according to the values of the parameter $\la$, the solutions are either a disc…

In this paper, we consider a class of structured nonconvex nonsmooth optimization problems, in which the objective function is formed by the sum of a possibly nonsmooth nonconvex function and a differentiable function whose gradient is…

The scope of this work is the constraint-based synthesis of termination arguments for the restricted class of programs called linear lasso programs. A termination argument consists of a ranking function as well as a set of supporting…

Assume that $X$ is a Banach space of measurable functions for which Koml\'os' Theorem holds. We associate to any closed convex bounded subset $C$ of $X$ a coefficient $t(C)$ which attains its minimum value when $C$ is closed for the…

We consider stochastic optimization problems involving an expected value of a nonlinear function of a base random vector and a conditional expectation of another function depending on the base random vector, a dependent random vector, and…

Set-functions appear in many areas of computer science and applied mathematics, such as machine learning, computer vision, operations research or electrical networks. Among these set-functions, submodular functions play an important role,…

We introduce a new invariant for subcategories X of finitely generated modules over a local ring R which we call the radius of X. We show that if R is a complete intersection and X is resolving, then finiteness of the radius forces X to…

Unsupervised rank aggregation on score-based permutations, which is widely used in many applications, has not been deeply explored yet. This work studies the use of submodular optimization for rank aggregation on score-based permutations in…

Let $G$ be a subgroup of $\mathrm{SL}(\mathbb{R}^{d+1})\ltimes\mathbb{R}^{d+1}$ obtained by adding a translation part to a torsion-free discrete subgroup of $\mathrm{SL}(\mathbb{R}^{d+1})$ dividing a convex cone in the sense of Benoist. We…

We develop a synthetic, variational framework for deriving comparison principles in infinite-dimensional Banach spaces. Unlike traditional approaches that rely on the regularity of minimizers and Euler--Lagrange equations, our method…

The first part of this work established the foundations of a radial duality between nonnegative optimization problems, inspired by the work of (Renegar, 2016). Here we utilize our radial duality theory to design and analyze projection-free…

Let V^L and V^R be simple vertex operator algebras satisfying certain natural uniqueness-of-vacuum, complete reducibility and cofiniteness conditions and let F be a conformal full field algebra over the tensor product of V^L and V^R. We…

Let $R$ be an algebra over a ring $\Bbbk$, $T$ an $R$-algebra, $M$ a finitely generated projective $R$-module, and $N$ a $T$-module. Let $G$ be a linearly reductive group scheme over $\Bbbk$ equipped with a representation…

This paper focuses on second-order necessary optimality conditions for constrained optimization problems on Banach spaces. For problems in the classical setting, where the objective function is $C^2$-smooth, we show that strengthened…

A new directional derivative and a new subdifferential for set-valued convex functions are constructed, and a set-valued version of the so-called 'max-formula' is proven. The new concepts are used to characterize solutions of convex…

This study presents the analytical formulation and the finite element solution of fractional order nonlocal plates under both Mindlin and Kirchoff formulations. By employing consistent definitions for fractional-order kinematic relations,…

A number of discrete and continuous optimization problems in machine learning are related to convex minimization problems under submodular constraints. In this paper, we deal with a submodular function with a directed graph structure, and…