Active set identification and rapid convergence for degenerate primal-dual problems[Paper][Code] (with M. Díaz, H. Lu, J. Yang), submitted to Mathematical Programming, 2026. Primal-dual optimization methods often exhibit a distinct two-stage behavior. Initially, they converge towards a solution at a sublinear rate. Then, after a certain point, all iterates accurately identify the set of active constraints, and their convergence accelerates to linear. We characterize mild conditions on the problem geometry and algorithm under which this phenomenon provably occurs. Our guarantees are entirely nonasymptotic and do not rely on strict complementarity (non-degeneracy).
Exact Classification of NMR Spectra from NMR Signals[Paper] (with C. A. Sing Long, M. Andía, A. Xavier), ICASSP 2024. We study whether exact spectra classification is possible from noisy spectroscopy data, depending on the quality of the measuring object (spectrometer). For any given external magnetic field of the spectrometer, we provide upper and lower bounds on the amount of adversarial electrical noise admissible for exact classification.
Towards Maximizing a Perceptual Sweet Spot for Spatial Sound With Loudspeakers[Paper][Code] (with C. A. Sing Long, R. Cádiz), IEEE Transactions on Audio, Speech, and Language Processing, 2022. We develop a first-principles mathematical framework and an efficient algorithm to solve a spatial-audio problem: rendering an auditory illusion over a region of interest with few speakers. To this end, we formulate a nonconvex nonsmooth variational problem and solve it using a layer-cake smoothing and difference-of-convex programming. In proof-of-concept numerical simulations, our method outperforms state-of-the-art sound field synthesis methods in terms of binaural azimuth localization and binaural coloration.
