Related papers: Subgradient Projection Operators
We make a review on the recent progress in the operator algebraic approach to (super)conformal field theory. We discuss representation theory, classification results, full and boundary conformal field theories, relations to supervertex…
We propose a new subgradient method for the minimization of nonsmooth convex functions over a convex set. To speed up computations we use adaptive approximate projections only requiring to move within a certain distance of the exact…
We introduce a relaxed-projection splitting algorithm for solving variational inequalities in Hilbert spaces for the sum of nonsmooth maximal monotone operators, where the feasible set is defined by a nonlinear and nonsmooth continuous…
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…
In this work, we propose and study a framework of generalized proximal point algorithms associated with a maximally monotone operator. We indicate sufficient conditions on the regularization and relaxation parameters of generalized proximal…
In a previous work of the authors, a result to algorithmically compute the topology types of the level curves of an algebraic surface, is given. From this result, here we derive applications based on level curves to determine some…
We introduce and investigate a new generalized convexity notion for functions called prox-convexity. The proximity operator of such a function is single-valued and firmly nonexpansive. We provide examples of (strongly) quasiconvex, weakly…
A survey of recents advances in the theory of Heun operators is offered. Some of the topics covered include: quadratic algebras and orthogonal polynomials, differential and difference Heun operators associated to Jacobi and Hahn…
We consider several differential operators on compact almost-complex, almost-Hermitian and almost-K\"ahler manifolds. We discuss Hodge Theory for these operators and a possible cohomological interpretation. We compare the associated spaces…
These notes contain a survey of some aspects of the theory of graded differential algebras and of noncommutative differential calculi as well as of some applications connected with physics. They also give a description of several new…
Operator learning has been highly successful for continuous mappings between infinite-dimensional spaces, such as PDE solution operators. However, many operators of interest-including differential operators-are discontinuous or set-valued,…
Formally symmetric differential operators on weighted Hardy-Hilbert spaces are analyzed, along with adjoint pairs of differential operators. Eigenvalue problems for such operators are rather special, but include many of the classical…
Optimization techniques have become increasingly critical due to the ever-growing model complexity and data scale. In particular, teleportation has emerged as a promising approach, which accelerates convergence of gradient descent-based…
The isomorphism between the reduction algebra and the invariant differential operators on G/H is sketched.
Many iterative methods in applied mathematics can be thought of as fixed-point iterations, and such algorithms are usually analyzed analytically, with inequalities. In this paper, we present a geometric approach to analyzing contractive and…
In this paper, we study a class of generalized monotone variational inequality (GMVI) problems whose operators are not necessarily monotone (e.g., pseudo-monotone). We present non-Euclidean extragradient (N-EG) methods for computing…
In this paper, we develop an enhanced version of the catching-up algorithm for sweeping processes through an appropriate concept of approximate projections. We establish some properties of this notion of approximate projection. Then, under…
The proximal gradient descent method, well-known for composite optimization, can be completely described by the concept of proximal gradient mapping. In this paper, we highlight our previous two discoveries of proximal gradient…
Variable projection solves structured optimization problems by completely minimizing over a subset of the variables while iterating over the remaining variables. Over the last 30 years, the technique has been widely used, with empirical and…
In this article, we study eigenvalue problems associated to self-adjoint operators and their approximation obtained by subspace projection, as used in the reduced basis method for instance. We provide error bounds between the exact…