Related papers: Limit points of the iterative scaling procedure
Computation of the large sparse matrix exponential has been an important topic in many fields, such as network and finite-element analysis. The existing scaling and squaring algorithm (SSA) is not suitable for the computation of the large…
Machine learning components commonly appear in larger decision-making pipelines; however, the model training process typically focuses only on a loss that measures accuracy between predicted values and ground truth values. Decision-focused…
The process of alternately row scaling and column scaling a positive $n \times n$ matrix $A$ converges to a doubly stochastic positive $n \times n$ matrix $S(A)$, called the \emph{Sinkhorn limit} of $A$. Exact formulae for the Sinkhorn…
We introduce a simple, intuitive and yet powerful algorithm for clustering analysis. This algorithm is an iterative process on the sample space, which arises as an extension of the iteratively generated correlation matrices. It allows for…
A $\textit{polygonal curve}$ is a collection of $m$ connected line segments specified as the linear interpolation of a list of points $\{p_0, p_1, \ldots, p_m\}$. These curves may be obtained by sampling points from an oriented curve in…
We present adaptive sequential SAA (sample average approximation) algorithms to solve large-scale two-stage stochastic linear programs. The iterative algorithm framework we propose is organized into \emph{outer} and \emph{inner} iterations…
We consider a discrete optimization formulation for learning sparse classifiers, where the outcome depends upon a linear combination of a small subset of features. Recent work has shown that mixed integer programming (MIP) can be used to…
The idea of unfolding iterative algorithms as deep neural networks has been widely applied in solving sparse coding problems, providing both solid theoretical analysis in convergence rate and superior empirical performance. However, for…
The importance of an adequate inner loop starting point (as opposed to a sufficient inner loop stopping rule) is discussed in the context of a numerical optimization algorithm consisting of nested primal-dual proximal-gradient iterations.…
This paper proposes an almost feasible Sequential Linear Programming (afSLP) algorithm. In the first part, the practical limitations of previously proposed Feasible Sequential Linear Programming (FSLP) methods are discussed along with…
Solving linear systems is a ubiquitous task in science and engineering. Because directly inverting a large-scale linear system can be computationally expensive, iterative algorithms are often used to numerically find the inverse. To…
Datalogo is an extension of Datalog that allows for aggregation and recursion over an arbitrary commutative semiring. Like Datalog, Datalogo programs can be evaluated via the natural iterative algorithm until a fixed point is reached.…
In the Internet of Things (IoT) community, Wireless Sensor Network (WSN) is a key technique to enable ubiquitous sensing of environments and provide reliable services to applications. WSN programs, typically interrupt-driven, implement the…
Decision-making problems in uncertain or stochastic domains are often formulated as Markov decision processes (MDPs). Policy iteration (PI) is a popular algorithm for searching over policy-space, the size of which is exponential in the…
Finding the sparset solution of an underdetermined system of linear equations $y=Ax$ has attracted considerable attention in recent years. Among a large number of algorithms, iterative thresholding algorithms are recognized as one of the…
We consider an infinite-dimensional stochastic clustering model on $\mathbb{R}$. In discrete time, each point of a unit-intensity simple point process moves halfway toward either of its left or right neighbors, chosen uniformly at random.…
In this paper, we investigate iterative methods that are based on sampling of the data for computing Tikhonov-regularized solutions. We focus on very large inverse problems where access to the entire data set is not possible all at once…
Iterative methods are commonly used approaches to solve large, sparse linear systems, which are fundamental operations for many modern scientific simulations. When the large-scale iterative methods are running with a large number of ranks…
In this paper, we propose iterative inner/outer approximations based on a recent notion of block factor-width-two matrices for solving semidefinite programs (SDPs). Our inner/outer approximating algorithms generate a sequence of upper/lower…
In this article, we establish a class of new projected type iteration methods based on matrix spitting for solving the linear complementarity problem. Also, we provide a sufficient condition for the convergence analysis when the system…