Newton method for ?0-regularized optimization

As a tractable approach, regularization is frequently adopted in sparse optimization. This gives rise to regularized optimization, which aims minimize the ?0 norm or its continuous surrogates that characterize sparsity. From continuity of discreteness norm, most challenging model ?0-regularized There an impressive body work on development numerical algorithms overcome this challenge. However, developed methods only ensure either (sub)sequence converges stationary point from deterministic optimization perspective distance between each iteration and any given reference bounded by error bound sense probability. In paper, we develop Newton-type method for prove generated sequence globally quadratically under standard assumptions, theoretically explaining our can perform surprisingly well.