Sparse recovery is a strategy for effectively reconstructing a signal by obtaining sparse
solutions of underdetermined linear systems. As an important feature of a signal, sparsity is …

In this paper, a new procedure, called generalized shrinkage conjugate gradient (GSCG), is
presented to solve the ℓ _1 ℓ 1-regularized convex minimization problem. In GSCG, we …

2,1 norm minimization with orthogonality constraints, which comprise a feasible region
called the Stiefel manifold, has wide applications in statistics and data science. The state-of …

Based on the memoryless BFGS (Broyden–Fletcher–Goldfarb–Shanno) updating formula of
a recent well-structured diagonal approximation of the Hessian, we propose an improved …

Low-rank matrix recovery from an observation data matrix has received considerable
attention in recent years, which has a wide range of applications in pattern recognition and …

Founded upon the scaled memoryless symmetric rank-one updating formula, we propose an
approximation of the Newton-type proximal strategy for minimizing the nonsmooth …

In real world, especially in the field of pattern recognition, a matrix formed from images,
visions, speech sounds or so forth under certain conditions usually subjects to a low-rank …

In the past decade, robust principal component analysis (RPCA) and low-rank matrix
completion (LRMC), as two very important optimization problems with the view of recovering …

As an effective strategy to enhance stochastic optimization, determining an appropriate step
size sequence when performing these algorithms has been warmly encouraged in solving …

In this study, we develop a nonmonotone variable metric Barzilai-Borwein method for
minimizing the sum of a smooth function and a convex, possibly nondifferentiable, function …