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The BFGS quasi-Newton methodology, popular for smooth minimization, has also proved surprisingly effective in nonsmooth optimization. Through a variety of simple examples and computational experiments, we explore how the BFGS matrix update…

The question of how to incorporate curvature information in stochastic approximation methods is challenging. The direct application of classical quasi- Newton updating techniques for deterministic optimization leads to noisy curvature…

This paper studies stochastic minimization of a finite-sum loss $ F (\mathbf{x}) = \frac{1}{N} \sum_{\xi=1}^N f(\mathbf{x};\xi) $. In many real-world scenarios, the Hessian matrix of such objectives exhibits a low-rank structure on a batch…

We consider the development of practical stochastic quasi-Newton, and in particular Kronecker-factored block-diagonal BFGS and L-BFGS methods, for training deep neural networks (DNNs). In DNN training, the number of variables and components…

Non-asymptotic analysis of quasi-Newton methods have gained traction recently. In particular, several works have established a non-asymptotic superlinear rate of $\mathcal{O}((1/\sqrt{t})^t)$ for the (classic) BFGS method by exploiting the…

In this paper we study stochastic quasi-Newton methods for nonconvex stochastic optimization, where we assume that noisy information about the gradients of the objective function is available via a stochastic first-order oracle (SFO). We…

We propose a new algorithm for the optimization of convex functions over a polyhedral set in Rn. The algorithm extends the spectral projected-gradient method with limited-memory BFGS iterates restricted to the present face whenever…

In a recent work, we introduced the foundations of an orthogonally constrained complete active space self-consistent field (OC-CASSCF) framework that produces state-specific molecular orbitals for mutually orthogonal multiconfigurational…

This paper considers the regularization continuation method and the trust-region updating strategy for the nonlinearly equality-constrained optimization problem. Namely, it uses the inverse of the regularization quasi-Newton matrix as the…

Recently several methods were proposed for sparse optimization which make careful use of second-order information [10, 28, 16, 3] to improve local convergence rates. These methods construct a composite quadratic approximation using Hessian…

In Part I of this work, we have proposed a general framework of decentralized stochastic quasi-Newton methods, which converge linearly to the optimal solution under the assumption that the local Hessian inverse approximations have bounded…

In this paper we study stochastic quasi-Newton methods for nonconvex stochastic optimization, where we assume that only stochastic information of the gradients of the objective function is available via a stochastic first-order oracle…

In this paper, a novel stochastic extra-step quasi-Newton method is developed to solve a class of nonsmooth nonconvex composite optimization problems. We assume that the gradient of the smooth part of the objective function can only be…

Linear programming relaxations are central to {\sc map} inference in discrete Markov Random Fields. The ability to properly solve the Lagrangian dual is a critical component of such methods. In this paper, we study the benefit of using…

We present an algorithm for minimizing a sum of functions that combines the computational efficiency of stochastic gradient descent (SGD) with the second order curvature information leveraged by quasi-Newton methods. We unify these…

Maximum entropy inference and learning of graphical models are pivotal tasks in learning theory and optimization. This work extends algorithms for these problems, including generalized iterative scaling (GIS) and gradient descent (GD), to…

In this paper, we propose an accelerated quasi-Newton proximal extragradient (A-QPNE) method for solving unconstrained smooth convex optimization problems. With access only to the gradients of the objective, we prove that our method can…

We introduce the decentralized Broyden-Fletcher-Goldfarb-Shanno (D-BFGS) method as a variation of the BFGS quasi-Newton method for solving decentralized optimization problems. The D-BFGS method is of interest in problems that are not well…

It has recently been shown that configuration state functions (CSF) with local orbitals can provide a compact reference state for low-spin open-shell electronic structures, such as antiferromagnetic states. However, optimizing a low-spin…

We propose a communication- and computation-efficient distributed optimization algorithm using second-order information for solving ERM problems with a nonsmooth regularization term. Current second-order and quasi-Newton methods for this…