A randomized sketching trust-region secant method for low-memory dynamic optimization

Vuchkov, Radoslav Georgiev; Kouri, Drew Philip

doi:10.1007/s11590-025-02216-2

A randomized sketching trust-region secant method for low-memory dynamic optimization

Journal Article · Wed Jun 25 00:00:00 EDT 2025 · Optimization Letters

DOI:https://doi.org/10.1007/s11590-025-02216-2· OSTI ID:2999462

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Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

The numerical solution of dynamic optimization problems is often limited by the memory required to store the state trajectory, which is used to evaluate the objective function and its derivatives. Recently, [R. Muthukumar et al., SIAM Journal on Optimization 31(2), pp. 1242–1275 (2021)] introduced a trust-region method for dynamic optimization that employs randomized sketching to compress the state trajectory, resulting in inexact derivative computations. By adaptively learning the sketch rank, the trust-region algorithm achieves rigorous convergence guarantees. Here, we extend this approach to use secant Hessian approximations. Due to the randomness introduced by the sketch, the traditional secant update formulae can produce poor Hessian approximations. In particular, the difference of two gradients, computed from two different sketches, may be inconsistent. To overcome this, we employ a sketched approximation of the Hessian application, in lieu of computing the gradient difference. We numerically demonstrate the improved stability of this approach on an example from PDE-constrained optimization.

View Accepted Manuscript (DOE)

Research Organization:: Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: NA0003525

OSTI ID:: 2999462

Report Number(s):: SAND--2025-12569J; 1742859

Journal Information:: Optimization Letters, Journal Name: Optimization Letters; ISSN 1862-4472; ISSN 1862-4480

Publisher:: Springer NatureCopyright Statement

Country of Publication:: United States

Language:: English

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A randomized sketching trust-region secant method for low-memory dynamic optimization

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References (27)

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