相关论文: Splitting algorithms and circuit analysis

We deal with various splitting methods in algebraic logic. The word `splitting' refers to splitting some of the atoms in a given relation or cylindric algebra each into one or more subatoms obtaining a bigger algebra, where the number of…

We present quantum algorithms for various problems related to graph connectivity. We give simple and query-optimal algorithms for cycle detection and odd-length cycle detection (bipartiteness) using a reduction to st-connectivity.…

An integral equation is a way to encapsulate the relationships between a function and its integrals. We develop a systematic way of describing Volterra integral equations -- specifically an algorithm that reduces any separable Volterra…

The theory of matrix splitting is a useful tool for finding solution of rectangular linear system of equations, iteratively. The purpose of this paper is two-fold. Firstly, we revisit theory of weak regular splittings for rectangular…

Nonlinear parabolic equations are frequently encountered in applications and efficient approximating techniques for their solution are of great importance. In order to provide an effective scheme for the temporal approximation of such…

In this paper, we propose an algorithm combining the forward-backward splitting method and the alternative projection method for solving the system of splitting inclusion problem. We want to find a point in the interception of a finite…

We propose and study a novel stochastic inertial primal-dual approach to solve composite optimization problems. These latter problems arise naturally when learning with penalized regularization schemes. Our analysis provide convergence…

In this paper, we address the scenario where nodes with sensor data are connected in a tree network, and every node wants to compute a given symmetric Boolean function of the sensor data. We first consider the problem of computing a…

While monotone operator theory is often studied on Hilbert spaces, many interesting problems in machine learning and optimization arise naturally in finite-dimensional vector spaces endowed with non-Euclidean norms, such as…

This paper (parts I and II) provides an expository introduction to monotone and near-monotone dynamical systems associated to biochemical networks, those whose graphs are consistent or near-consistent. Many conclusions can be drawn from…

This paper proposes a two-point inertial proximal point algorithm to find zero of maximal monotone operators in Hilbert spaces. We obtain weak convergence results and non-asymptotic $O(1/n)$ convergence rate of our proposed algorithm in…

The partitioning of a system model will condition the structure of the controller as well as its design. In order to partition a system model, one has to know what states and inputs to group together to define subsystem models. For a given…

Consider a set of networked agents endowed with private cost functions and seeking to find a consensus on the minimizer of the aggregate cost. A new class of random asynchronous distributed optimization methods is introduced. The methods…

Conventionally, one calculates a zero in a beta function by computing this function to a given loop order and solving for the zero. Here we discuss a different method which is applicable in theories where one can perform a partial…

Operator-splitting methods are widely used to solve differential equations, especially those that arise from multi-scale or multi-physics models, because a monolithic (single-method) approach may be inefficient or even infeasible. The most…

This paper presents the first in a series of results that allow us to develop a theory providing finer control over the complexity of normalisation, and in particular of cut elimination. By considering atoms as self-dual non-commutative…

We describe, study, and experiment with an algorithm for finding all solutions of systems of polynomial equations using homotopy continuation and monodromy. This algorithm follows a framework developed in previous work and can operate in…

We address the problem of finding the zeros of the sum of a maximally monotone operator and a cocoercive operator. Our approach introduces a modification to the forward-backward method by integrating an inertial/momentum term alongside a…

We present a novel matrix-parametrized frugal splitting algorithm which finds the zero of a sum of maximal monotone and cocoercive operators composed with linear selection operators. We also develop a semidefinite programming framework for…

We introduce the theory of operator monotone functions and employ it to derive a new inequality relating the quantum relative entropy and the quantum conditional entropy. We present applications of this new inequality and in particular we…