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In this paper, we study matrix scaling and balancing, which are fundamental problems in scientific computing, with a long line of work on them that dates back to the 1960s. We provide algorithms for both these problems that, ignoring…
This paper examines the nonconvex quadratically constrained quadratic programming (QCQP) problems using an iterative method. One of the existing approaches for solving nonconvex QCQP problems relaxes the rank one constraint on the unknown…
In this paper we present the solver DuQuad specialized for solving general convex quadratic problems arising in many engineering applications. When it is difficult to project on the primal feasible set, we use the (augmented) Lagrangian…
Model predictive control (MPC) is a powerful framework for optimal control of dynamical systems. However, MPC solvers suffer from a high computational burden that restricts their application to systems with low sampling frequency. This…
Training modern deep learning models is increasingly constrained by GPU memory and compute limits. While Randomized Numerical Linear Algebra (RandNLA) offers proven techniques to compress these models, the lack of a unified,…
Decentralized optimization algorithms are important in different contexts, such as distributed optimal power flow or distributed model predictive control, as they avoid central coordination and enable decomposition of large-scale problems.…
We present a general-purpose interior-point solver for convex optimization problems with conic constraints. Our method is based on a homogeneous embedding method originally developed for general monotone complementarity problems and more…
The emergence of energy harvesting devices creates the potential for batteryless sensing and computing devices. Such devices operate only intermittently, as energy is available, presenting a number of challenges for software developers.…
In this paper, we propose an inexact Augmented Lagrangian Method (ALM) for the optimization of convex and nonsmooth objective functions subject to linear equality constraints and box constraints where errors are due to fixed-point data. To…
This documentation is designed for beginners in Graphics Processing Unit (GPU)-programming and who want to get familiar with OpenACC and OpenMP offloading models. Here we present an overview of these two programming models as well as of the…
We present a quantum algorithm for solving algebraic Riccati equations, with applications to quantum-chemical random-phase approximation (RPA) and higher-order RPA theories. Our method block-encodes stabilizing Riccati solutions via Riesz…
This paper proposes an open-source distributed solver for solving Sparse Convex Optimization (SCO) problems over computational networks. Motivated by past algorithmic advances in mixed-integer optimization, the Sparse Convex Optimization…
A software platform for global optimisation, called PaGMO, has been developed within the Advanced Concepts Team (ACT) at the European Space Agency, and was recently released as an open-source project. PaGMO is built to tackle…
The development of the mlpack C++ machine learning library (http://www.mlpack.org/) has required the design and implementation of a flexible, robust optimization system that is able to solve the types of arbitrary optimization problems that…
Constrained non-convex optimization problems frequently arise in control applications. Solving such problems is inherently challenging, as existing methods often converge to suboptimal local minima or incur prohibitive computational costs.…
Minimax optimization has become a central tool in machine learning with applications in robust optimization, reinforcement learning, GANs, etc. These applications are often nonconvex-nonconcave, but the existing theory is unable to identify…
In this two-part paper, we propose a general algorithmic framework for the minimization of a nonconvex smooth function subject to nonconvex smooth constraints. The algorithm solves a sequence of (separable) strongly convex problems and…
Quadratic programming (QP) is a fundamental optimization model with wide-ranging applications in decision-making and machine learning, yet efficiently solving large-scale instances remains a major computational challenge. Building upon the…
In this paper we study a nonconvex-strongly-concave constrained minimax problem. Specifically, we propose a first-order augmented Lagrangian method for solving it, whose subproblems are nonconvex-strongly-concave unconstrained minimax…
Effectively encoding inequality constraints is a primary obstacle in applying quantum algorithms to financial optimization. A quantum model for Markowitz portfolio optimization is presented that resolves this by embedding slack variables…