Related papers: Polynomial Linear Programming with Gaussian Belief…
Belief propagation is a well-studied algorithm for approximating local marginals of multivariate probability distribution over complex networks, while tensor network states are powerful tools for quantum and classical many-body problems.…
We present a proximal augmented Lagrangian based solver for general convex quadratic programs (QPs), relying on semismooth Newton iterations with exact line search to solve the inner subproblems. The exact line search reduces in this case…
We present a short step interior point method for solving a class of nonlinear programming problems with quadratic objective function. Convex quadratic programming problems can be reformulated as problems in this class. The method is shown…
A Gaussian process (GP) is a powerful and widely used regression technique. The main building block of a GP regression is the covariance kernel, which characterizes the relationship between pairs in the random field. The optimization to…
Optimization plays a central role in modern radiation therapy, where it is used to determine optimal treatment machine parameters in order to deliver precise doses adapted to each patient case. In general, solving the optimization problems…
Applying an interior-point method to the central-path conditions is a widely used approach for solving quadratic programs. Reformulating these conditions in the log-domain is a natural variation on this approach that to our knowledge is…
Linear Programming is now included in Algorithm undergraduate and postgraduate courses for Computer Science majors. It is possible to teach interior-point methods directly with just minimal knowledge of Algebra and Matrices.
Learning to optimize is a rapidly growing area that aims to solve optimization problems or improve existing optimization algorithms using machine learning (ML). In particular, the graph neural network (GNN) is considered a suitable ML model…
This paper explores two condensed-space interior-point methods to efficiently solve large-scale nonlinear programs on graphics processing units (GPUs). The interior-point method solves a sequence of symmetric indefinite linear systems, or…
We present a new view of Gaussian belief propagation (GaBP) based on a representation of the determinant as a product over orbits of a graph. We show that the GaBP determinant estimate captures totally backtracking orbits of the graph and…
We consider the estimation of an i.i.d.\ random vector observed through a linear transform followed by a componentwise, probabilistic (possibly nonlinear) measurement channel. A novel algorithm, called generalized approximate message…
We consider the problem of learning a sparse graph underlying an undirected Gaussian graphical model, a key problem in statistical machine learning. Given $n$ samples from a multivariate Gaussian distribution with $p$ variables, the goal is…
Message-passing algorithms based on the Belief Propagation (BP) equations constitute a well-known distributed computational scheme. It is exact on tree-like graphical models and has also proven to be effective in many problems defined on…
The emergence of huge-scale, data-intensive linear optimization (LO) problems in applications such as machine learning has driven the need for more computationally efficient interior point methods (IPMs). While conventional IPMs are…
A fundamental computation for statistical inference and accurate decision-making is to compute the marginal probabilities or most probable states of task-relevant variables. Probabilistic graphical models can efficiently represent the…
We propose an inexact infeasible arc-search interior-point method for solving linear optimization problems. The method combines an arc-search strategy with inexact solutions to Newton systems and admits a polynomial iteration complexity…
Backward propagation of errors (backpropagation) is a method to minimize objective functions (e.g., loss functions) of deep neural networks by identifying optimal sets of weights and biases. Imposing constraints on weight precision is often…
The focus in this work is on interior-point methods for inequality-constrained quadratic programs, and particularly on the system of nonlinear equations to be solved for each value of the barrier parameter. Newton iterations give high…
We design and analyze primal-dual, feasible interior-point algorithms (IPAs) employing full Newton steps to solve convex optimization problems in standard conic form. Unlike most nonsymmetric cone programming methods, the algorithms…
We develop a new `subspace layered least squares' interior point method (IPM) for solving linear programs. Applied to an $n$-variable linear program in standard form, the iteration complexity of our IPM is up to an $O(n^{1.5} \log n)$…