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Second-Order Optimization via Quiescence Trajectory Tracing
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DOI：10.1109/tcsi.2026.3689681.png)
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Abstract
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Circuit simulation has developed robust numerical methods to achieve fast DC operating point convergence in highly nonlinear systems. Similar challenges arise in nonconvex optimization, where second-order optimization methods often require restrictive step sizes to ensure a monotonically decreasing objective function. Moreover, in the presence of nonlinear objective functions with large Lipschitz constants, increasingly small step-sizes become a bottleneck to fast convergence. Building on established connections between optimization and circuit dynamics, we explore the application of fast DC circuit simulation methods to second-order optimization. Using a dynamic system representation of the trajectory of optimization variables, we exploit the quiescence of the dynamical system to determine the steady state that coincides with the critical point of the objective function. This optimization via quiescence uses a variation of the quasi-steady state analysis method in ACES to adaptively select large step-sizes that sequentially follow each optimization variable to a quasi-steady state until all state variables reach the actual steady state. The result is a second-order optimization method that utilizes large step-sizes and does not require a monotonically decreasing objective function to reach a critical point. Experimentally, we demonstrate the use of this fast DC circuit simulation for optimizing nonconvex problems in general unconstrained optimization problems including a power systems example and compare them to existing state-of-the-art second-order methods, including damped Newton-Raphson, Broyden–Fletcher–Goldfarb–Shanno (BFGS), and Symmetric Rank 1 (SR1).
Keywords:
Optimization algorithms
optimization
quasi-steady state
differential-algebraic systems
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