Related papers: MPAX: Mathematical Programming in JAX
In this paper, we consider the nonconvex quadratically constrained quadratic programming (QCQP) with one quadratic constraint. By employing the conjugate gradient method, an efficient algorithm is proposed to solve QCQP that exploits the…
Population balance equation (PBE) models have potential to automate many engineering processes with far-reaching implications. In the pharmaceutical sector, crystallization model-based design can contribute to shortening excessive drug…
This paper is concerned with the problem of exact MAP inference in general higher-order graphical models by means of a traditional linear programming relaxation approach. In fact, the proof that we have developed in this paper is a rather…
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…
We solve large-scale mixed-integer linear programs (MILPs) via distributed asynchronous saddle point computation. This is motivated by the MILPs being able to model problems in multi-agent autonomy, e.g., task assignment problems and…
We implement a trust region method on the GPU for nonlinear least squares curve fitting problems using a new deep learning Python library called JAX. Our open source package, JAXFit, works for both unconstrained and constrained curve…
Mathematical Program with Complementarity Constraints (MPCC) plays a very important role in many fields such as engineering design, economic equilibrium, multilevel game, and mathematical programming theory itself. In theory its constraints…
Among numerical libraries capable of computing gradient descent optimization, JAX stands out by offering more features, accelerated by an intermediate representation known as Jaxpr language. However, editing the Jaxpr code is not directly…
We present CHAP (Coordinating Heuristics Across Platforms) a GPU-CPU-hybrid primal heuristic framework for mixed-integer programming. CHAP adopts a portfolio approach where it coordinates a set of primal heuristics, including Local Search,…
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…
While many approaches have been proposed to analyze the problem of matrix multiplication parallel computing, few of them address the problem on heterogeneous processor platforms. It still remains an open question on heterogeneous processor…
Process mining provides powerful insights into organizational workflows, but extracting these insights typically requires expertise in specialized query languages and data science tools. Large Language Models (LLMs) offer the potential to…
Many areas of machine learning and science involve large linear algebra problems, such as eigendecompositions, solving linear systems, computing matrix exponentials, and trace estimation. The matrices involved often have Kronecker,…
Mixed Integer Programming (MIP) is one of the most widely used modeling techniques for combinatorial optimization problems. In many applications, a similar MIP model is solved on a regular basis, maintaining remarkable similarities in model…
Approximate linear programming (ALP) is an efficient approach to solving large factored Markov decision processes (MDPs). The main idea of the method is to approximate the optimal value function by a set of basis functions and optimize…
Implicit neural representations with multi-layer perceptrons (MLPs) have recently gained prominence for a wide variety of tasks such as novel view synthesis and 3D object representation and rendering. However, a significant challenge with…
Deploying large language models (LLMs) for online inference is often constrained by limited GPU memory, particularly due to the growing KV cache during auto-regressive decoding. Hybrid GPU-CPU execution has emerged as a promising solution…
Distributing spatially located heterogeneous workloads is an important problem in parallel scientific computing. We investigate the problem of partitioning such workloads (represented as a matrix of non-negative integers) into rectangles,…
Efficiently serving Large Language Models (LLMs) requires selecting an optimal parallel execution plan, balancing computation, memory, and communication overhead. However, determining the best strategy is challenging due to varying…
In this paper, we mainly study one class of convex mixed-integer nonlinear programming problems (MINLPs) with non-differentiable data. By dropping the differentiability assumption, we substitute gradients with subgradients obtained from KKT…