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