Related papers: Design and implementation of a modular interior-po…
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…
Nonconvex mixed-integer nonlinear programs (MINLPs) represent a challenging class of optimization problems that often arise in engineering and scientific applications. Because of nonconvexities, these programs are typically solved with…
This paper presents the Julia package CCOpt, built on top of the interior-point solver MadNLP. CCOpt implements a suite of algorithms for Mathematical Programs with Complementarity Constraints (MPCCs). The solver additionally comes with…
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…
Linear programming (LP) is an extremely useful tool which 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 practice, non-specialized interior point algorithms often cannot utilize the massively parallel compute resources offered by modern many- and multi-core compute platforms. However, efficient distributed solution techniques are required,…
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…
Interior-point algorithms constitute a very interesting class of algorithms for solving linear-programming problems. In this paper we study efficient implementations of such algorithms for solving the linear program that appears in the…
The advent of efficient interior point optimization methods has enabled the tractable solution of large-scale linear and nonlinear programming (NLP) problems. A prominent example of such a method is seen in Ipopt, a widely-used, open-source…
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…
We address the solution of Mixed Integer Linear Programming (MILP) models with strong relaxations that are derived from Dantzig-Wolfe decompositions and allow a pseudo-polynomial pricing algorithm. We exploit their network-flow…
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…
An interior-point algorithm framework is proposed, analyzed, and tested for solving nonlinearly constrained continuous optimization problems. The main setting of interest is when the objective and constraint functions may be nonlinear…
SQP and interior-point methods (also referred to as Lagrange-Newton methods) typically share key algorithmic components, such as strategies for computing descent directions and mechanisms that promote global convergence. Building on this…
The ADMM-based interior point (ABIP, Lin et al. 2021) method is a hybrid algorithm that effectively combines interior point method (IPM) and first-order methods to achieve a performance boost in large-scale linear optimization. Different…
Interior point methods (IPMs) are a common approach for solving linear programs (LPs) with strong theoretical guarantees and solid empirical performance. The time complexity of these methods is dominated by the cost of solving a linear…
Trajectory optimization is the core of modern model-based robotic control and motion planning. Existing trajectory optimizers, based on sequential quadratic programming (SQP) or differential dynamic programming (DDP), are often limited by…
The Interior-Point Methods are a class for solving linear programming problems that rely upon the solution of linear systems. At each iteration, it becomes important to determine how to solve these linear systems when the constraint matrix…
In this paper, we introduce two parabolic target-space interior-point algorithms for solving monotone linear complementarity problems. The first algorithm is based on a universal tangent direction, which has been recently proposed for…
Interior point methods are among the most popular techniques for large scale nonlinear optimization, owing to their intrinsic ability of scaling to arbitrary large problem sizes. Their efficiency has attracted in recent years a lot of…