相关论文: On Weak Tractability of the Clenshaw-Curtis Smolya…
We develop a stochastic integration theory for predictable integrands with respect to a L\'evy basis. Our approach is based on decoupling inequalities for tangent sequences and reduces the construction of the stochastic integral essentially…
We consider minimizing a function consisting of a quadratic term and a proximable term which is possibly nonconvex and nonsmooth. This problem is also known as scaled proximal operator. Despite its simple form, existing methods suffer from…
In this paper we investigate the well-posedness of the Cauchy problem for a Schr\"odinger operator with singular lower order terms. We allow distributional coefficients and we approach this problem via the regularising methods at the core…
Variational regularisation is the primary method for solving inverse problems, and recently there has been considerable work leveraging deeply learned regularisation for enhanced performance. However, few results exist addressing the…
We study the approximation of compact linear operators defined over certain weighted tensor product Hilbert spaces. The information complexity is defined as the minimal number of arbitrary linear functionals which is needed to obtain an…
We introduce a particular optimization problem that minimizes the sum of a non-convex quadratic function and logarithmic barrier-functions in a $\ell_\infty$-trust-region (i.e. cube). Our paper covers three topics. We explain the relevance…
Many practical optimization problems lack strong convexity. Fortunately, recent studies have revealed that first-order algorithms also enjoy linear convergences under various weaker regularity conditions. While the relationship among…
This paper concerns the minimization of the composition of a nonsmooth convex function and a $\mathcal{C}^{1,1}$ mapping $F$ over a $\mathcal{C}^2$-smooth embedded closed submanifold $\mathcal{M}$. For this class of nonconvex and nonsmooth…
We propose a nonsmooth trust-region method for solving optimization problems with locally Lipschitz continuous functions, with application to problems constrained by variational inequalities of the second kind. Under suitable assumptions on…
This is the first part of a two-part paper describing a new concept of separation of variables applied to the Clebsch integrable case of the Kirchhoff equations. There are two principal novelties: 1) Separating coordinates are constructed…
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 introduce constraints necessary for type checking a higher-order concurrent constraint language, and solve them with an incremental algorithm. Our constraint system extends rational unification by constraints x$\subseteq$ y saying that…
In machine learning it is common to interpret each data point as a vector in Euclidean space. However the data may actually be functional i.e.\ each data point is a function of some variable such as time and the function is discretely…
The problem of deciding whether CSP instances admit solutions has been deeply studied in the literature, and several structural tractability results have been derived so far. However, constraint satisfaction comes in practice as a…
We derive computationally tractable formulations of the robust counterparts of convex quadratic and conic quadratic constraints that are concave in matrix-valued uncertain parameters. We do this for a broad range of uncertainty sets. In…
We establish a new family of Carleman inequalities for wave operators on cylindrical spacetime domains containing a potential that is critically singular, diverging as an inverse square on all the boundary of the domain. These estimates are…
In this paper, we consider solving a class of nonconvex and nonsmooth problems frequently appearing in signal processing and machine learning research. The traditional alternating direction method of multipliers encounters troubles in both…
This note is concerned with the problem of minimizing a separable, convex, composite (smooth and nonsmooth) function subject to linear constraints. We study a randomized block-coordinate interpretation of the Chambolle-Pock primal-dual…
We develop a new theory of strong subalgebras and linear congruences that are defined globally. Using this theory we provide a new proof of the correctness of Zhuk's algorithm for all tractable CSPs on a finite domain, and therefore a new…
We consider analytically weak solutions to semilinear stochastic partial differential equations with non-anticipating coefficients driven by cylindrical Brownian motion. The solutions are allowed to take values in general separable Banach…