An algorithm framework of sparse minimization for positive definite quadratic forms

• An algorithm framework of sparse minimization for PDQF is proposed.
• The convergence to global minimum is proved.
• Its computational complexity is analyzed and compared with FISTA.
• Some well-known methods are illustrated to be optimized by the proposed algorithm.
• Illustrative experiments show that SRC and LASSO via the proposed method converges quickly.

Many well-known machine learning and pattern recognition methods can be seen as special cases of sparse minimization of Positive Definite Quadratic Forms (PDQF). An algorithm framework of sparse minimization is proposed for PDQF. It is theoretically analyzed to converge to global minimum. The computational complexity is analyzed and compared with the state-of-the-art Fast Iterative Shrinkage-Thresholding Algorithm (FISTA). Some well-known machine learning and pattern recognition methods are illustrated to be optimized by the proposed algorithm framework. Illustrative experiments show that Sparse Representation Classification (SRC) and Least Absolute Shrinkage and Selection Operator (LASSO) via the proposed method converges much faster than several classical methods.