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math.OC2024
Novel Limited Memory Quasi-Newton Methods Based On Optimal Matrix Approximation
Erik Berglund, Mikael Johansson
Update formulas for the Hessian approximations in quasi-Newton methods such as BFGS can be derived as analytical solutions to certain nearest-matrix problems. In this article, we p…
math.OC2024
Soft quasi-Newton: Guaranteed positive definiteness by relaxing the secant constraint
Erik Berglund, Jiaojiao Zhang, Mikael Johansson
We propose a novel algorithm, termed soft quasi-Newton (soft QN), for optimization in the presence of bounded noise. Traditional quasi-Newton algorithms are vulnerable to such pert…