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A general-purpose C++ software program called $\mathbb{CGPOPS}$ is described for solving multiple-phase optimal control problems using adaptive Gaussian quadrature collocation. The software employs a Legendre-Gauss-Radau direct orthogonal…

There is an increasing interest in quantum algorithms for optimization problems. Within convex optimization, interior-point methods and other recently proposed quantum algorithms are non-trivial to implement on noisy quantum devices. Here,…

This paper studies two fundamental problems in power systems: the economic dispatch problem (EDP) and load shedding. For the EDP, an extension of the problem considering the transmission losses is presented. Because the optimization problem…

This paper considers smooth convex optimization problems with many functional constraints. To solve this general class of problems we propose a new stochastic perturbed augmented Lagrangian method, called SGDPA, where a perturbation is…

We develop an algorithm to solve tridiagonal systems of linear equations, which appear in implicit finite-difference schemes of partial differential equations (PDEs), being the time-dependent Schr\"{o}dinger equation (TDSE) an ideal…

We have formulated the problem of generating periodic dense paritcle packings as an optimization problem called the Adaptive Shrinking Cell (ASC) formulation [S. Torquato and Y. Jiao, Phys. Rev. E {\bf 80}, 041104 (2009)]. Because the…

Semidefinite programming (SDP) is a central topic in mathematical optimization with extensive studies on its efficient solvers. In this paper, we present a proof-of-principle sublinear-time algorithm for solving SDPs with low-rank…

In the realm of distributed systems tasked with managing and processing large-scale graph-structured data, optimizing graph partitioning stands as a pivotal challenge. The primary goal is to minimize communication overhead and runtime cost.…

This paper presents a novel algorithm integrating global and robust optimization methods to solve continuous non-convex quadratic problems under convex uncertainty sets. The proposed Robust spatial branch-and-bound (RsBB) algorithm combines…

In this paper, we utilize stochastic optimization to reduce the space complexity of convex composite optimization with a nuclear norm regularizer, where the variable is a matrix of size $m \times n$. By constructing a low-rank estimate of…

The nonlinear programming (NLP) problem to solve distribution-level optimal power flow (D-OPF) poses convergence issues and does not scale well for unbalanced distribution systems. The existing scalable D-OPF algorithms either use…

We present self-supervised geometric perception (SGP), the first general framework to learn a feature descriptor for correspondence matching without any ground-truth geometric model labels (e.g., camera poses, rigid transformations). Our…

This article describes a geometric partitioning software that can be used for quick computation of data partitions on many-core HPC machines. It is most suited for dynamic applications with load distributions that vary with time.…

In this paper, we introduce a technique to enhance the computational efficiency of solution algorithms for high-dimensional discrete simulation-based optimization problems. The technique is based on innovative adaptive partitioning…

We study nonlinear constrained optimization problems in which only function evaluations of the objective and constraints are available. Existing zeroth-order methods rely on noisy gradient and Jacobian surrogates in high dimensions, making…

Root mean square propagation (abbreviated as RMSProp) is a first-order stochastic algorithm used in machine learning widely. In this paper, a stable gradient-adjusted RMSProp (abbreviated as SGA-RMSProp) with mini-batch stochastic gradient…

Semidefinite programs (SDP) are one of the most versatile frameworks in numerical optimization, serving as generalizations of many conic programs and as relaxations of NP-hard combinatorial problems. Their main drawback is their…

Stochastic gradient descent (SGD) now acts as a fundamental part of optimization in current machine learning. Meanwhile, deep learning architectures have shown outstanding performance in a wide range of fields, such as natural language…

Optimization over the Stiefel manifold is a fundamental computational problem in many scientific and engineering applications. Despite considerable research effort, high-dimensional optimization problems over the Stiefel manifold remain…

Several recent empirical studies demonstrate that important machine learning tasks, e.g., training deep neural networks, exhibit low-rank structure, where the loss function varies significantly in only a few directions of the input space.…