Smooth active manifold

Alternating Iteratively Reweighted \(\ell_1\) and Subspace Newton Algorithms for Nonconvex Sparse Optimization

  • Xiangyu Yang
    • Categories Nonlinear Optimization, Nonsmooth Optimization Tags , ,

    This paper presents a novel hybrid algorithm for minimizing the sum of a continuously differentiable loss function and a nonsmooth, possibly nonconvex, sparsity‑promoting regularizer. The proposed method adaptively switches between solving a reweighted \(\ell_1\)-regularized subproblem and performing an inexact subspace Newton step. The reweighted \(\ell_1\)-subproblem admits an efficient closed-form solution via the soft-thresholding operator, thereby … Read more

    Efficient QUIC-Based Damped Inexact Iterative Reweighting for Sparse Inverse Covariance Estimation with Nonconvex Partly Smooth Regularization

  • Xiangyu Yang
    • Categories Constrained Nonlinear Optimization, Nonsmooth Optimization, Semi-definite Programming Tags , , ,

    In this paper, we study sparse inverse covariance matrix estimation incorporating partly smooth nonconvex regularizers. To solve the resulting regularized log-determinant problem, we develop DIIR-QUIC—a novel Damped Inexact Iteratively Reweighted algorithm based on QUadratic approximate Inverse Covariance (QUIC) method. Our approach generalizes the classic iteratively reweighted \(\ell_1\) scheme through damped fixed-point updates. A key novelty … Read more