Related papers: linrax: A JAX Compatible, Simplex Method Linear Pr…
We introduce Lineax, a library bringing linear solves and linear least-squares to the JAX+Equinox scientific computing ecosystem. Lineax uses general linear operators, and unifies linear solves and least-squares into a single,…
We present MPAX (Mathematical Programming in JAX), an open-source first-order solver for large-scale linear programming (LP) and convex quadratic programming (QP) built natively in JAX. The primary goal of MPAX is to exploit modern machine…
Explicit solutions to optimal control problems are rarely obtainable. Of particular interest are the explicit solutions derived for minimax problems, providing a framework to address adversarial conditions and uncertainty. This work…
Solving large dense linear systems and eigenvalue problems is a core requirement in many areas of scientific computing, but scaling these operations beyond a single GPU remains challenging within modern programming frameworks. While highly…
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…
We present an implementation of interval analysis and mixed monotone interval reachability analysis as function transforms in Python, fully composable with the computational framework JAX. The resulting toolbox inherits several key features…
We introduce Optimistix: a nonlinear optimisation library built in JAX and Equinox. Optimistix introduces a novel, modular approach for its minimisers and least-squares solvers. This modularity relies on new practical abstractions for…
The simplex method is one of the most fundamental technologies for solving linear programming (LP) problems and has been widely applied to different practical applications. In the past literature, how to improve and accelerate the simplex…
Mixed-precision training has emerged as an indispensable tool for enhancing the efficiency of neural network training in recent years. Concurrently, JAX has grown in popularity as a versatile machine learning toolbox. However, it currently…
Velocity Planning for self-driving vehicles in a complex environment is one of the most challenging tasks. It must satisfy the following three requirements: safety with regards to collisions; respect of the maximum velocity limits defined…
Unlimited, or so-called helpful-only language models are trained without safety alignment constraints and never refuse user queries. They are widely used by leading AI companies as internal tools for red teaming and alignment evaluation.…
The Framework for Unified and Robust data Analysis with JAX (Furax) is an open-source Python framework for modeling data acquisition systems and solving inverse problems in astrophysics and cosmology. Built on JAX, Furax provides composable…
We consider continuous linear programs over a continuous finite time horizon $T$, with a constant coefficient matrix, linear right hand side functions and linear cost coefficient functions, where we search for optimal solutions in the space…
This paper presents fast first-order methods for solving linear programs (LPs) approximately. We adapt online linear programming algorithms to offline LPs and obtain algorithms that avoid any matrix multiplication. We also introduce a…
The linear programming (LP) approach is, together with value iteration and policy iteration, one of the three fundamental methods to solve optimal control problems in a dynamic programming setting. Despite its simple formulation,…
In this short paper we present a linear constraint solver for the UniCalc system, an environment for reliable solution of mathematical modeling problems.
We propose a novel Linear Program (LP) based formula- tion for solving jigsaw puzzles. We formulate jigsaw solving as a set of successive global convex relaxations of the stan- dard NP-hard formulation, that can describe both jigsaws with…
We present lrux, a JAX-based software package for fast low-rank updates of determinants and Pfaffians, targeting the dominant computational bottleneck in various quantum Monte Carlo (QMC) algorithms. The package implements efficient…
We describe an efficient implementation of a recent simplex-type algorithm for the exact solution of separated continuous linear programs, and compare it with linear programming approximation of these problems obtained via discretization of…
Linear Programming (LP) is widely applied in industry and is a key component of various other mathematical problem-solving techniques. Recent work introduced an LP compiler translating polynomial-time, polynomial-space algorithms into…