A General and Streamlined Differentiable Optimization Framework

• URL: http://arxiv.org/abs/2510.25986v1
• Date: Wed, 29 Oct 2025 21:42:36 GMT
• Title: A General and Streamlined Differentiable Optimization Framework
• Authors: Andrew W. Rosemberg, Joaquim Dias Garcia, François Pacaud, Robert B. Parker, Benoît Legat, Kaarthik Sundar, Russell Bent, Pascal Van Hentenryck,
• Abstract summary: This paper presents the DiffOptl interface for Julia optimization framework.<n>A first-class JuMP-native API allows users to obtain named parameters derivatives directly with respect to them.<n>Results demonstrate that differentiing a routine can be as a training tool for experimentation, learning, and design-without deviating from standard JuMP modeling practices.
• Score: 10.851559133306196
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: Differentiating through constrained optimization problems is increasingly central to learning, control, and large-scale decision-making systems, yet practical integration remains challenging due to solver specialization and interface mismatches. This paper presents a general and streamlined framework-an updated DiffOpt.jl-that unifies modeling and differentiation within the Julia optimization stack. The framework computes forward - and reverse-mode solution and objective sensitivities for smooth, potentially nonconvex programs by differentiating the KKT system under standard regularity assumptions. A first-class, JuMP-native parameter-centric API allows users to declare named parameters and obtain derivatives directly with respect to them - even when a parameter appears in multiple constraints and objectives - eliminating brittle bookkeeping from coefficient-level interfaces. We illustrate these capabilities on convex and nonconvex models, including economic dispatch, mean-variance portfolio selection with conic risk constraints, and nonlinear robot inverse kinematics. Two companion studies further demonstrate impact at scale: gradient-based iterative methods for strategic bidding in energy markets and Sobolev-style training of end-to-end optimization proxies using solver-accurate sensitivities. Together, these results demonstrate that differentiable optimization can be deployed as a routine tool for experimentation, learning, calibration, and design-without deviating from standard JuMP modeling practices and while retaining access to a broad ecosystem of solvers.

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