Multi-way data arises in many applications such as electroencephalography classification, face recognition, text mining and hyperspectral data analysis. Tensor decomposition has been commonly used to find the hidden factors and elicit the intrinsic structures of the multi-way data. This paper considers sparse nonnegative Tucker decomposition (NTD), which is to decompose a given tensor into the product of a core tensor and several factor matrices with sparsity and nonnegativity constraints. An alternating proximal gradient method is applied to solve the problem. The algorithm is then modified to sparse NTD with missing values. Per-iteration cost of the algorithm is estimated scalable about the data size, and global convergence is established under fairly loose conditions. Numerical experiments on both synthetic and real world data demonstrate its superiority over a few state-of-the-art methods for (sparse

In this ar ti cle, the authors de vel oped an al ter na tive meth od ol ogy to cal cu late theoption- adjusted spread for the mortgage- backed se cu ri ties us ing par tial dif fer ential equa tion tech nique. The nu meri cal im ple men ta tion is dis cussed in de tail, includ ing the con ver gence and er ror analy sis. This ap proach pro vides us a fast andac cu rate way to pric ing MBS.

The support vector machine (SVM) was originally designed for binary classifications. A lot of effort has been put to generalize the binary SVM to multiclass SVM (MSVM) which are more complex problems. Initially, MSVMs were solved by considering their dual formulations which are quadratic programs and can be solved by standard second-order methods. However, the duals of MSVMs with regularizers are usually more difficult to formulate and computationally very expensive to solve. This paper focuses on several regularized MSVMs and extends the alternating direction method of multiplier (ADMM) to these MSVMs. Using a splitting technique, all considered MSVMs are written as two-block convex programs, for which the ADMM has global convergence guarantees. Numerical experiments on synthetic and real data demonstrate the high efficiency and accuracy of our algorithms.

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We provide an affirmative answer to an question that the Fischer-Burmeister complementarity function associated with symmetric cones, named the FB SC complementarity function, is globally Lipschitz continuous and strongly semismooth everywhere for Hn and Qn. This is achieved with the help of embedding Hn and Qn into certain Sm.