Related papers: PPD-IPM: Outer primal, inner primal-dual interior-…
We propose a new framework to implement interior point method (IPM) to solve very large linear programs (LP). Traditional IPMs typically use Newton's method to approximately solve a subproblem that aims to minimize a log-barrier penalty…
This paper deals with Interior Point Methods (IPMs) for Optimal Control Problems (OCPs) with pure state and mixed constraints. This paper establishes a complete proof of convergence of IPMs for a general class of OCPs. Convergence results…
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…
Linear programming (LP) is an extremely useful tool and has been successfully applied to solve various problems in a wide range of areas, including operations research, engineering, economics, or even more abstract mathematical areas such…
In this paper we propose an efficient distributed algorithm for solving loosely coupled convex optimization problems. The algorithm is based on a primal-dual interior-point method in which we use the alternating direction method of…
The interior-point method (IPM) has become the workhorse method for nonlinear programming. The performance of IPM is directly related to the linear solver employed to factorize the Karush--Kuhn--Tucker (KKT) system at each iteration of the…
The emergence of huge-scale, data-intensive linear optimization (LO) problems in applications such as machine learning has driven the need for more computationally efficient interior point methods (IPMs). While conventional IPMs are…
This work develops new algorithms with rigorous efficiency guarantees for infinite horizon imitation learning (IL) with linear function approximation without restrictive coherence assumptions. We begin with the minimax formulation of the…
Several algorithms are available in the literature for finding the entire set of Pareto-optimal solutions in MultiObjective Linear Programming (MOLP). However, it has not been proposed so far an interior point algorithm that finds all…
Sequential quadratic programming and sequential convex programming efficiently solve nonlinear programs (NLPs) by linearizing inner nonlinearities while preserving the outer convex structure. This paper introduces a sequential mixed-integer…
Primal-dual interior-point methods solve constrained convex optimization problems to tight tolerances with speed and robustness. Their solutions are also efficiently differentiable with respect to the problem data through the implicit…
Primal-Dual Interior-Point methods are capable of solving constrained convex optimization problems to tight tolerances in a fast and robust manner. The derivatives of the primal-dual solution with respect to the problem matrices can be…
We present a numerical method for the local solution of nonlinear programming problems. The SUMT approach of Fiacco and McCormick results in a merit function with quadratic penalties and logarithmic barriers. Our NLP solver works by…
We consider the minimum-norm-point (MNP) problem over polyhedra, a well-studied problem that encompasses linear programming. We present a general algorithmic framework that combines two fundamental approaches for this problem: active set…
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,…
Distributed and decentralized optimization are key for the control of networked systems. Application examples include distributed model predictive control and distributed sensing or estimation. Non-linear systems, however, lead to problems…
This paper presents PIQP, a high-performance toolkit for solving generic sparse quadratic programs (QP). Combining an infeasible Interior Point Method (IPM) with the Proximal Method of Multipliers (PMM), the algorithm can handle…
Quantum computing has attracted significant interest in the optimization community because it potentially can solve classes of optimization problems faster than conventional supercomputers. Several researchers proposed quantum computing…
The use of quantum computing to accelerate complex optimization problems is a burgeoning research field. This paper applies Quantum Linear System Algorithms (QLSAs) to Newton systems within Interior Point Methods (IPMs) to take advantage of…
Quantum linear system algorithms (QLSAs) have the potential to speed up algorithms that rely on solving linear systems. Interior Point Methods (IPMs) yield a fundamental family of polynomial-time algorithms for solving optimization…