Doubly majorized algorithm for sparsity-inducing optimization problems with regularizer-compatible constraints

We consider a class of sparsity-inducing optimization problems whose constraint set is regularizer-compatible, in the sense that, becomes easy-to-project-onto after coordinate transformation induced by regularizer. Our model general enough to cover, as special cases, ordered LASSO Tibshirani and Suo (Technometrics 58:415–423, 2016) its variants with some commonly used nonconvex regularizers. The presence both regularizer poses challenges on design efficient algorithms. In this paper, exploiting absolute-value symmetry other properties regularizer, we propose new algorithm, called doubly majorized algorithm (DMA), for problems. DMA makes use projections onto each iteration, hence can be performed efficiently. Without invoking any qualification conditions such those based horizon subdifferentials, show that accumulation point sequence generated so-called $$\psi _\textrm{opt}$$ -stationary point, notion stationarity define inspired L-stationarity Beck Eldar (SIAM J Optim 23:1480–1509, 2013) Hallak (Math Oper Res 41:196–223, . also global minimizer our has again without imposing conditions. Finally, illustrate numerically performance solving