Related papers: Condensed-space methods for nonlinear programming …
While interior point methods have been the centerpiece of nonlinear programming tools used in science and engineering, their reliance on linear solvers that can tackle sparse symmetric indefinite and highly ill-conditioned problems made it…
This work focuses on the iterative solution of sequences of KKT linear systems arising in interior point methods applied to large convex quadratic programming problems. This task is the computational core of the interior point procedure 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 solution of sparse symmetric positive definite linear systems is an important computational kernel in large-scale scientific and engineering modeling and simulation. We will solve the linear systems using a direct method, in which a…
We propose a novel preconditioned inexact primal-dual interior point method for constrained convex quadratic programming problems. The algorithm we describe invokes the preconditioned conjugate gradient method on a new reduced Schur…
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).…
We propose a method for solving Karush-Kuhn-Tucker (KKT) systems that exploits block triangular submatrices by first using a Schur complement decomposition to isolate the block triangular submatrices then performing a block backsolve where…
Semidefinite programs (SDPs) are powerful theoretical tools that have been studied for over two decades, but their practical use remains limited due to computational difficulties in solving large-scale, realistic-sized problems. In this…
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 apply novel inner-iteration preconditioned Krylov subspace methods to the interior-point algorithm for linear programming (LP). Inner-iteration preconditioners recently proposed by Morikuni and Hayami enable us to overcome the severe…
In this paper, we address the efficient numerical solution of linear and quadratic programming problems, often of large scale. With this aim, we devise an infeasible interior point method, blended with the proximal method of multipliers,…
In this work, we introduce an interior-point method that employs tensor decompositions to efficiently represent and manipulate the variables and constraints of semidefinite programs, targeting problems where the solutions may not be…
Linear solvers are major computational bottlenecks in a wide range of decision support and optimization computations. The challenges become even more pronounced on heterogeneous hardware, where traditional sparse numerical linear algebra…
In this paper, we propose an infeasible arc-search interior-point algorithm for solving nonlinear programming problems. Most algorithms based on interior-point methods are categorized as line search, since they compute a next iterate on a…
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…
We present a fully Julia-based, GPU-accelerated workflow for solving large-scale sparse nonlinear optimal control problems. Continuous-time dynamics are modeled and then discretized via direct transcription with \texttt{OptimalControl.jl}…
Preconditioned Krylov subspace (KSP) methods are widely used for solving large-scale sparse linear systems arising from numerical solutions of partial differential equations (PDEs). These linear systems are often nonsymmetric due to the…
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…
We are interested in solving linear systems arising from three applications: (1) kernel methods in machine learning, (2) discretization of boundary integral equations from mathematical physics, and (3) Schur complements formed in the…
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…