Related papers: A block symmetric Gauss-Seidel decomposition theor…
In this paper, we present a two-phase augmented Lagrangian method, called QSDPNAL, for solving convex quadratic semidefinite programming (QSDP) problems with constraints consisting of a large number of linear equality, inequality…
In open quantum systems with strong symmetries, the global scaled cumulant generating function (SCGF) is generally nonanalytic, so the G\"artner-Ellis theorem cannot directly yield the genuine large-deviation rate function. To address this…
We present an overlapping Schwarz decomposition algorithm for constrained quadratic programs (QPs). Schwarz algorithms have been traditionally used to solve linear algebra systems arising from partial differential equations, but we have…
We consider the problem of identifying underlying community-like structures in graphs. Towards this end we study the Stochastic Block Model (SBM) on $k$-clusters: a random model on $n=km$ vertices, partitioned in $k$ equal sized clusters,…
Spline functions are smooth piecewise polynomials widely used for interpolation and smoothing, and nonnegative spline smoothing is also studied for nonnegative data. Previous research used sufficient conditions for the nonnegativity of…
We propose a quantum-assisted framework for solving constrained finite-horizon nonlinear optimal control problems using a barrier Sequential Quadratic Programming (SQP) approach. Within this framework, a quantum subroutine is incorporated…
This paper considers a fractional programming problem (P) which minimizes a ratio of quadratic functions subject to a two-sided quadratic constraint. As is well-known, the fractional objective function can be replaced by a parametric family…
A series of hybrid quantum-classical generalized Benders decomposition (GBD) algorithms are proposed to address unit commitment (UC) problems under centralized, distributed, and partially distributed frameworks. In the centralized approach,…
Quasi-Newton (QN) methods provide an efficient alternative to second-order methods for minimizing smooth unconstrained problems. While QN methods generally compose a Hessian estimate based on one secant interpolation per iteration,…
The block classical Gram--Schmidt (BCGS) algorithm and its reorthogonalized variant are widely-used methods for computing the economic QR factorization of block columns $X$ due to their lower communication cost compared to other approaches…
We consider semidefinite programming (SDP) for the binary stochastic block model with equal-sized communities. Prior work of Hajek, Wu, and Xu proposed an SDP (sym-SDP) for the symmetric case where the intra-community edge probabilities are…
The {\sc $c$-Balanced Separator} problem is a graph-partitioning problem in which given a graph $G$, one aims to find a cut of minimum size such that both the sides of the cut have at least $cn$ vertices. In this paper, we present new…
We introduce a verification framework to exactly verify the worst-case performance of sequential convex programming (SCP) algorithms for parametric non-convex optimization. The verification problem is formulated as an optimization problem…
This paper studies the effective convergence of iterative methods for solving convex minimization problems using block Gauss--Seidel algorithms. It investigates whether it is always possible to algorithmically terminate the iteration in…
On modern large-scale parallel computers, the performance of Krylov subspace iterative methods is limited by global synchronization. This has inspired the development of $s$-step Krylov subspace method variants, in which iterations are…
The goal of this paper is to derive new classes of valid convex inequalities for quadratically constrained quadratic programs (QCQPs) through the technique of lifting. Our first main result shows that, for sets described by one bipartite…
This paper addresses the problem of solving nonlinear systems in the context of symmetric quantum signal processing (QSP), a powerful technique for implementing matrix functions on quantum computers. Symmetric QSP focuses on representing…
In this paper, we consider a bilevel polynomial optimization problem where the objective and the constraint functions of both the upper and the lower level problems are polynomials. We present methods for finding its global minimizers and…
This paper presents a stochastic block-coordinate proximal Newton method for minimizing the sum of a blockwise Lipschitz-continuously differentiable function and a separable nonsmooth convex function. At each iteration, the method randomly…
High dimensional unconstrained quadratic programs (UQPs) involving massive datasets are now common in application areas such as web, social networks, etc. Unless computational resources that match up to these datasets are available, solving…