{"ID":2879286,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2508.16094","arxiv_id":"2508.16094","title":"GPU Implementation of Second-Order Linear and Nonlinear Programming Solvers","abstract":"In recent years, GPU-accelerated optimization solvers based on second-order methods (e.g., interior-point methods) have gained momentum with the advent of mature and efficient GPU-accelerated direct sparse linear solvers, such as cuDSS. This paper provides an overview of the state of the art in GPU-based second-order solvers, focusing on pivoting-free interior-point methods for large and sparse linear and nonlinear programs. We begin by highlighting the capabilities and limitations of the currently available GPU-accelerated sparse linear solvers. Next, we discuss different formulations of the Karush-Kuhn-Tucker systems for second-order methods and evaluate their suitability for pivoting-free GPU implementations. We also discuss strategies for computing sparse Jacobians and Hessians on GPUs for nonlinear programming. Finally, we present numerical experiments demonstrating the scalability of GPU-based optimization solvers. We observe speedups often exceeding 10x compared to comparable CPU implementations on large-scale instances when solved up to medium precision. Additionally, we examine the current limitations of existing approaches.","short_abstract":"In recent years, GPU-accelerated optimization solvers based on second-order methods (e.g., interior-point methods) have gained momentum with the advent of mature and efficient GPU-accelerated direct sparse linear solvers, such as cuDSS. This paper provides an overview of the state of the art in GPU-based second-order s...","url_abs":"https://arxiv.org/abs/2508.16094","url_pdf":"https://arxiv.org/pdf/2508.16094v2","authors":"[\"Alexis Montoison\",\"François Pacaud\",\"Sungho Shin\",\"Mihai Anitescu\"]","published":"2025-08-22T05:19:50Z","proceeding":"math.OC","tasks":"[\"math.OC\"]","methods":"[]","has_code":false}