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We propose a general random subspace framework for unconstrained nonconvex optimization problems that requires a weak probabilistic assumption on the subspace gradient, which we show to be satisfied by various random matrix ensembles, such…
We approach the Max-3-Cut problem through the lens of maximizing complex-valued quadratic forms and demonstrate that low-rank structure in the objective matrix can be exploited, leading to alternative algorithms to classical semidefinite…
This paper investigates regularity, controllability and observability for a networked dynamic system (NDS) with its subsystems being described in a descriptor form and system matrices of each subsystem being represented by a generalized…
In real-world applications, it is important for machine learning algorithms to be robust against data outliers or corruptions. In this paper, we focus on improving the robustness of a large class of learning algorithms that are formulated…
Semidefinite programs (SDPs) are convex optimization programs with vast applications in control theory, quantum information, combinatorial optimization and operational research. Noisy intermediate-scale quantum (NISQ) algorithms aim to make…
We present a semidefinite program (SDP) algorithm to find eigenvalues of Schr\"{o}dinger operators within the bootstrap approach to quantum mechanics. The bootstrap approach involves two ingredients: a nonlinear set of constraints on the…
We introduce and analyze Structured Stochastic Zeroth order Descent (S-SZD), a finite difference approach that approximates a stochastic gradient on a set of $l\leq d$ orthogonal directions, where $d$ is the dimension of the ambient space.…
We study the inverse problem of estimating n locations $t_1, ..., t_n$ (up to global scale, translation and negation) in $R^d$ from noisy measurements of a subset of the (unsigned) pairwise lines that connect them, that is, from noisy…
We propose LeAP-SSN (Levenberg--Marquardt Adaptive Proximal Semismooth Newton method), a semismooth Newton-type method with a simple, parameter-free globalisation strategy that guarantees convergence from arbitrary starting points in…
We propose a stochastic variance-reduced cubic regularized Newton algorithm to optimize the finite-sum problem over a Riemannian submanifold of the Euclidean space. The proposed algorithm requires a full gradient and Hessian update at the…
This paper proposes and develops new Newton-type methods to solve structured nonconvex and nonsmooth optimization problems with justifying their fast local and global convergence by means of advanced tools of variational analysis and…
Generalizing earlier work characterizing the quantum query complexity of computing a function of an unknown classical ``black box'' function drawn from some set of such black box functions, we investigate a more general quantum query model…
The Nelson-Siegel-Svensson (NSS) interest rate curve model yields a separable nonlinear least-squares problem whose inner linear block is often ill-conditioned because the basis functions become nearly collinear. We analyze this instability…
Sorting is a foundational primitive of computer science and optimizations in sorting subroutines can cascade into significant performance gains for high-throughput systems. In this paper, we analyze the inefficiencies of a non-comparison…
Semidefinite programs (SDPs) are a framework for exact or approximate optimization that have widespread application in quantum information theory. We introduce a new method for using reductions to construct integrality gaps for SDPs. These…
In this paper, we propose a low-rank coordinate descent approach to structured semidefinite programming with diagonal constraints. The approach, which we call the Mixing method, is extremely simple to implement, has no free parameters, and…
Fractional Burgers equations pose substantial challenges for classical numerical methods due to the combined effects of nonlocality and shock-forming nonlinear dynamics. In particular, linear approximation frameworks-such as spectral,…
A stochastic-gradient-based interior-point algorithm for minimizing a continuously differentiable objective function (that may be nonconvex) subject to bound constraints is presented, analyzed, and demonstrated through experimental results.…
Stochastic gradient descent (SGD) is a promising method for solving large-scale inverse problems, due to its excellent scalability with respect to data size. In this work, we analyze a new data-driven regularized stochastic gradient descent…
In this paper we study the problem of characterizing and computing the nonanticipative rate distortion function (NRDF) for partially observable multivariate Gauss-Markov processes with hard mean squared error (MSE) distortion constraints.…