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The dominant contribution to communication complexity in factorizing a matrix using QR with column pivoting is due to column-norm updates that are required to process pivot decisions. We use randomized sampling to approximate this process…
Sequential quadratic programming (SQP) is widely used in solving nonlinear optimization problem, with advantages of warm-starting solutions, as well as finding high-accurate solution and converging quadratically using second-order…
Layer factorization has emerged as a widely used technique for training memory-efficient neural networks. However, layer factorization methods face several challenges, particularly a lack of robustness during the training process. To…
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…
In this paper, we present efficient solutions for the nonlinear program (NLP) associated with nonlinear model predictive control (NMPC) by leveraging the linear parameter-varying (LPV) embedding of nonlinear models and sequential quadratic…
Matrix Factorization (MF) has been widely applied in machine learning and data mining. A large number of algorithms have been studied to factorize matrices. Among them, stochastic gradient descent (SGD) is a commonly used method.…
In this article, a globally convergent sequential quadratic programming (SQP) method is developed for multi-objective optimization problems with inequality type constraints. A feasible descent direction is obtained using a linear…
We present a general-purpose solver for convex quadratic programs based on the alternating direction method of multipliers, employing a novel operator splitting technique that requires the solution of a quasi-definite linear system with the…
This paper proposes a control algorithm for stable implementation of asynchronous parallel quadratic programming (PQP) through dual decomposition technique. In general, distributed and parallel optimization requires synchronization of data…
The QR factorization and the SVD are two fundamental matrix decompositions with applications throughout scientific computing and data analysis. For matrices with many more rows than columns, so-called "tall-and-skinny matrices," there is a…
In this paper, we propose a parallel shooting algorithm for solving nonlinear model predictive control problems using sequential quadratic programming. This algorithm is built on a two-phase approach where we first test and assess…
Rank-revealing matrix decompositions provide an essential tool in spectral analysis of matrices, including the Singular Value Decomposition (SVD) and related low-rank approximation techniques. QR with Column Pivoting (QRCP) is usually…
This paper focuses on the design of sequential quadratic optimization (commonly known as SQP) methods for solving large-scale nonlinear optimization problems. The most computationally demanding aspect of such an approach is the computation…
In this paper, we concentrate on a particular category of quadratically constrained quadratic programming (QCQP): nonconvex QCQP with one equality constraint. This type of QCQP problem optimizes a quadratic objective under a fixed…
As multicore systems continue to gain ground in the High Performance Computing world, linear algebra algorithms have to be reformulated or new algorithms have to be developed in order to take advantage of the architectural features on these…
Quadratic programming (QP) forms a crucial foundation in optimization, encompassing a broad spectrum of domains and serving as the basis for more advanced algorithms. Consequently, as the scale and complexity of modern applications continue…
The Sequential Linear Quadratic (SLQ) algorithm is a continuous-time variant of the well-known Differential Dynamic Programming (DDP) technique with a Gauss-Newton Hessian approximation. This family of methods has gained popularity in the…
This paper proposes two quantum operation scheduling methods for accelerating parallel state-vector-based quantum circuit simulation using multiple graphics processing units (GPUs). The proposed methods reduce all-to-all communication…
The QR algorithm is one of the three phases in the process of computing the eigenvalues and the eigenvectors of a dense nonsymmetric matrix. This paper describes a task-based QR algorithm for reducing an upper Hessenberg matrix to real…
In this paper, we analyze the convergence as well as the rate of convergence of asynchronous distributed quadratic programming (QP) with dual decomposition technique. In general, distributed optimization requires synchronization of data at…