Related papers: linrax: A JAX Compatible, Simplex Method Linear Pr…
Linear programming (LP) relaxations are widely employed in exact solution methods for multilinear programs (MLP). One example is the family of Recursive McCormick Linearization (RML) strategies, where bilinear products are substituted for…
It has been shown that the parallel Lattice Linear Predicate (LLP) algorithm solves many combinatorial optimization problems such as the shortest path problem, the stable marriage problem and the market clearing price problem. In this…
Numerical simulations are ubiquitous in mathematics and computational science. Several industrial and clinical applications entail modeling complex multiphysics systems that evolve over a variety of spatial and temporal scales. This study…
The lattice Boltzmann method (LBM) has emerged as a prominent technique for solving fluid dynamics problems due to its algorithmic potential for computational scalability. We introduce XLB library, a Python-based differentiable LBM library…
Despite major advancements in nonlinear programming (NLP) and convex relaxations, most system operators around the world still predominantly use some form of linear programming (LP) approximation of the AC power flow equations. This is…
In robot control, planning, and learning, there is a need for rigid-body dynamics libraries that are highly performant, easy to use, and compatible with CPUs and accelerators. While existing libraries often excel at either low-latency CPU…
It is well known that the most challenging question in optimization and discrete geometry is whether there is a strongly polynomial time simplex algorithm for linear programs (LPs). This paper gives a positive answer to this question by…
This paper introduces JaxPruner, an open-source JAX-based pruning and sparse training library for machine learning research. JaxPruner aims to accelerate research on sparse neural networks by providing concise implementations of popular…
Linear superiorization considers linear programming problems but instead of attempting to solve them with linear optimization methods it employs perturbation resilient feasibility-seeking algorithms and steers them toward reduced (not…
A linear program with linear complementarity constraints (LPCC) requires the minimization of a linear objective over a set of linear constraints together with additional linear complementarity constraints. This class has emerged as a…
In this work, we focus on separable convex optimization problems with linear and box constraints and compute the solution in closed-form as a function of some Lagrange multipliers that can be easily computed in a finite number of…
We present msmJAX, a Python package implementing the multilevel summation method with B-spline interpolation, a linear-scaling algorithm for efficiently evaluating electrostatic and other long-range interactions in particle-based…
System Level Synthesis (SLS) parametrization facilitates controller synthesis for large, complex, and distributed systems by incorporating system level constraints (SLCs) into a convex SLS problem and mapping its solution to stable…
Biological and advanced cyberphysical control systems often have limited, sparse, uncertain, and distributed communication and computing in addition to sensing and actuation. Fortunately, the corresponding plants and performance…
In this paper we solve mixed-integer linear programs (MILPs) via distributed asynchronous saddle point computation. This work is motivated by the MILPs being able to model problems in multi-agent autonomy, such as task assignment problems…
We propose relational linear programming, a simple framework for combing linear programs (LPs) and logic programs. A relational linear program (RLP) is a declarative LP template defining the objective and the constraints through the logical…
Many problems in machine learning can be solved by rounding the solution of an appropriate linear program (LP). This paper shows that we can recover solutions of comparable quality by rounding an approximate LP solution instead of the ex-…
We consider linear programming (LP) problems in infinite dimensional spaces that are in general computationally intractable. Under suitable assumptions, we develop an approximation bridge from the infinite-dimensional LP to tractable finite…
In this paper we introduce an open-source software package written in C++ for efficiently finding solutions to quadratic programming problems with linear complementarity constraints. These problems arise in a wide range of applications in…
In this paper, we study the problem of optimizing a linear program whose variables are the answers to a conjunctive query. For this we propose the language LP(CQ) for specifying linear programs whose constraints and objective functions…