English
Related papers

Related papers: Parallel Interior-Point Solver for Block-Structure…

200 papers

We propose an implementation of an interior-point-based nonlinear predictive controller on a heterogeneous processor. The workload can be split between a general-purpose CPU and a field-programmable gate array to trade off the contradicting…

Systems and Control · Computer Science 2018-07-11 Bulat Khusainov , Eric C. Kerrigan , Andrea Suardi , George A. Constantinides

We present a new algorithm for convex separable quadratic programming (QP) called Nys-IP-PMM, a regularized interior-point solver that uses low-rank structure to accelerate solution of the Newton system. The algorithm combines the interior…

Optimization and Control · Mathematics 2025-01-15 Ya-Chi Chu , Luiz-Rafael Santos , Madeleine Udell

Solving optimization problems is the key to decision making in many real-life analytics applications. However, the coefficients of the optimization problems are often uncertain and dependent on external factors, such as future demand or…

Neural and Evolutionary Computing · Computer Science 2020-10-28 Jayanta Mandi , Tias Guns

Spatial Branch and Bound (B&B) algorithms are widely used for solving nonconvex problems to global optimality, yet they remain computationally expensive. Though some works have been carried out to speed up B&B via CPU parallelization, GPU…

Optimization and Control · Mathematics 2025-07-29 Hongzhen Zhang , Tim Kerkenhoff , Neil Kichler , Manuel Dahmen , Alexander Mitsos , Uwe Naumann , Dominik Bongartz

Given a non-convex optimization problem, we study conditions under which every Karush-Kuhn-Tucker (KKT) point is a global optimizer. This property is known as KT-invexity and allows to identify the subset of problems where an interior point…

Optimization and Control · Mathematics 2017-07-07 Ksenia Bestuzheva , Hassan Hijazi

The classical method to solve a quadratic optimization problem with nonlinear equality constraints is to solve the Karush-Kuhn-Tucker (KKT) optimality conditions using Newton's method. This approach however is usually computationally…

Optimization and Control · Mathematics 2016-03-17 Tuan T. Nguyen , Mircea Lazar , Hans Butler

Efficient ordinary differential equation solvers for chemical kinetics must take into account the available thread and instruction-level parallelism of the underlying hardware, especially on many-core coprocessors, as well as the numerical…

Computational Physics · Physics 2018-03-28 Christopher P. Stone , Andrew T. Alferman , Kyle E. Niemeyer

Solving constrained nonlinear programs (NLPs) is of great importance in various domains such as power systems, robotics, and wireless communication networks. One widely used approach for addressing NLPs is the interior point method (IPM).…

Optimization and Control · Mathematics 2024-10-22 Xi Gao , Jinxin Xiong , Akang Wang , Qihong Duan , Jiang Xue , Qingjiang Shi

Solving inverse problems and achieving statistical rigour in landscape evolution models requires running many model realizations. Parallel computation is necessary to achieve this in a reasonable time. However, no previous algorithm is…

Computational Engineering, Finance, and Science · Computer Science 2019-01-23 Richard Barnes

This paper considers a nonconvex optimization problem that evolves over time, and addresses the synthesis and analysis of regularized primal-dual gradient methods to track a Karush-Kuhn-Tucker (KKT) trajectory. The proposed regularized…

Optimization and Control · Mathematics 2018-12-04 Yujie Tang , Emiliano Dall'Anese , Andrey Bernstein , Steven Low

Most linear algebra kernels in interior point methods for linear programming require the solution of linear systems of equation with the matrix $N = A^TD^{-1}A$ (or $AD^{-1}A^T$), where $A$ denotes the constraint matrix of the linear…

Numerical Analysis · Mathematics 2017-08-17 Robert Luce

We propose a solution strategy for linear systems arising in interior method optimization, which is suitable for implementation on hardware accelerators such as graphical processing units (GPUs). The current gold standard for solving these…

Optimization and Control · Mathematics 2026-03-09 Shaked Regev , Nai-Yuan Chiang , Eric Darve , Cosmin G. Petra , Michael A. Saunders , Kasia Świrydowicz , Slaven Peleš

The work of Wachter and Biegler suggests that infeasible-start interior point methods (IPMs) developed for linear programming cannot be adapted to nonlinear optimization without significant modification, i.e., using a two-phase or penalty…

Optimization and Control · Mathematics 2018-01-12 Oliver Hinder , Yinyu Ye

Numerically solving ordinary differential equations (ODEs) is a naturally serial process and as a result the vast majority of ODE solver software are serial. In this manuscript we developed a set of parallelized ODE solvers using…

Numerical Analysis · Mathematics 2022-09-13 Utkarsh , Chris Elrod , Yingbo Ma , Christopher Rackauckas

The conic bundle implementation of the spectral bundle method for large scale semidefinite programming solves in each iteration a semidefinite quadratic subproblem by an interior point approach. For larger cutting model sizes the limiting…

Optimization and Control · Mathematics 2023-08-25 Christoph Helmberg

The main objective of this work consists in analyzing sub-structuring method for the parallel solution of sparse linear systems with matrices arising from the discretization of partial differential equations such as finite element, finite…

Numerical Analysis · Mathematics 2021-08-31 Abal-Kassim Cheik Ahamed , Frédéric Magoulès

We introduce a new algorithm for solving unconstrained discrete-time optimal control problems. Our method follows a direct multiple shooting approach, and consists of applying the SQP method together with an $\ell_2$ augmented Lagrangian…

Optimization and Control · Mathematics 2024-07-02 João Sousa-Pinto , Dominique Orban

In this paper we theoretically show that interior-point methods based on self-concordant barriers possess favorable global complexity beyond their standard application area of convex optimization. To do that we propose first- and…

Optimization and Control · Mathematics 2024-04-30 Pavel Dvurechensky , Mathias Staudigl

In this paper, we proposed an interior point method for constrained optimization, which is characterized by the using of quasi-tangential subproblem. This algorithm follows the main ideas of primal dual interior point methods and…

Optimization and Control · Mathematics 2015-09-10 Songqiang Qiu , Zhongwen Chen

The growing demand for solving large-scale, data-intensive linear and conic optimization problems, particularly in applications such as artificial intelligence and machine learning, has highlighted the limitations of classical interior…