Related papers: HAMSI: A Parallel Incremental Optimization Algorit…
We propose a continuous-time second-order optimization algorithm for solving unconstrained convex optimization problems with bounded Hessian. We show that this alternative algorithm has a comparable convergence rate to that of the…
We describe a quantum algorithm based on an interior point method for solving a linear program with $n$ inequality constraints on $d$ variables. The algorithm explicitly returns a feasible solution that is $\varepsilon$-close to optimal,…
In this paper, we revisit the large-scale constrained linear regression problem and propose faster methods based on some recent developments in sketching and optimization. Our algorithms combine (accelerated) mini-batch SGD with a new…
In recent years, considerable attention has been devoted to the regularization models due to the presence of high-dimensional data in scientific research. Sparse support vector machine (SVM) are useful tools in high-dimensional data…
The Metropolis-Hastings algorithm allows one to sample asymptotically from any probability distribution $\pi$. There has been recently much work devoted to the development of variants of the MH update which can handle scenarios where such…
This paper proposes a parallel numerical algorithm to simulate the flow and the transport in a discrete fracture network taking into account the mass exchanges with the surrounding matrix. The discretization of the Darcy fluxes is based on…
To construct a parallel approach for solving optimization problems with orthogonality constraints is usually regarded as an extremely difficult mission, due to the low scalability of the orthonormalization procedure. However, such demand is…
Gaussian Process Regression (GPR) is a nonparametric supervised learning method, widely valued for its ability to quantify uncertainty. Despite its advantages and broad applications, classical GPR implementations face significant…
This paper introduces the design and implementation of two parallel dual simplex solvers for general large scale sparse linear programming problems. One approach, called PAMI, extends a relatively unknown pivoting strategy called…
In this paper, we introduce a Homogeneous Second-Order Descent Method (HSODM) using the homogenized quadratic approximation to the original function. The merit of homogenization is that only the leftmost eigenvector of a gradient-Hessian…
We propose a multistage method for making inference at all levels of a Bayesian hierarchical model (BHM) using natural data partitions to increase efficiency by allowing computations to take place in parallel form using software that is…
We describe a second-order accurate approach to sparsifying the off-diagonal blocks in the hierarchical approximate factorizations of sparse symmetric positive definite matrices. The norm of the error made by the new approach depends…
We consider concave minimization problems over non-convex sets.Optimization problems with this structure arise in sparse principal component analysis. We analyze both a gradient projection algorithm and an approximate Newton algorithm where…
We consider minimizing finite-sum and expectation objective functions via Hessian-averaging based subsampled Newton methods. These methods allow for gradient inexactness and have fixed per-iteration Hessian approximation costs. The recent…
Stochastic gradient descent type methods are ubiquitous in machine learning, but they are only applicable to the optimization of differentiable functions. Proximal algorithms are more general and applicable to nonsmooth functions. We…
We propose an efficient ADMM method with guarantees for high-dimensional problems. We provide explicit bounds for the sparse optimization problem and the noisy matrix decomposition problem. For sparse optimization, we establish that the…
The existing machine learning algorithms for minimizing the convex function over a closed convex set suffer from slow convergence because their learning rates must be determined before running them. This paper proposes two machine learning…
Scalable algorithms to solve optimization and regression tasks even approximately, are needed to work with large datasets. In this paper we study efficient techniques from matrix sketching to solve a variety of convex constrained regression…
We propose a novel parallel algorithm for decomposing hard CircuitSAT instances. The technique employs specialized constraints to partition an original SAT instance into a family of weakened formulas. Our approach is implemented as a…
Hierarchical optimization refers to problems with interdependent decision variables and objectives, such as minimax and bilevel formulations. While various algorithms have been proposed, existing methods and analyses lack adaptivity in…