A nonmonotone ADMM-based diagonal quasi-Newton update with application to the compressive sensing problem

    Zohre Aminifard   Affiliation
    ; Saman Babaie-Kafaki   Affiliation


Considering a minimization problem according to the Byrd-Nocedal measure function together with the secant equation, a diagonal quasi-Newton updating formula is suggested. To find the optimal elements of the updating matrix, the well-known algorithm of the alternating direction method of multipliers (ADMM) is employed. Moreover, convergence analysis is conducted based on a modified nonmonotone Armijo line search incorporating the simulated annealing strategy. Lastly, performance of the method is numerically tested on a set of CUTEr functions and on a smooth transcendental approximation of the compressive sensing problem. Across the computational spectrum, the given method turns out to be successful.

Keyword : large-scale optimization, quasi-Newton update, ADMM strategy, nonmonotone line search, simulated annealing, compressive sensing, smoothing technique

How to Cite
Aminifard, Z., & Babaie-Kafaki, S. (2023). A nonmonotone ADMM-based diagonal quasi-Newton update with application to the compressive sensing problem. Mathematical Modelling and Analysis, 28(4), 673–688.
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Oct 20, 2023
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