Learning new representations in machine learning is often tackled using a factorization of the data. For many such problems, including sparse coding and matrix completion, learning these factorizations can be difficult, in terms of efficiency and to guarantee that the solution is a global minimum. Recently, a general class of objectives have been introduced, called induced regularized factor mo...

Distributions of bending stiffness along the spans of laminated composite shafts are determined via a non-destructive evaluation approach. The finite element method formulated on the assumption of uniform bending stiffness within each element is used in the deflection analysis of the shafts. Differences between measured and theoretically predicted deflections at any two points on a shaft are us...

It is known that there are feasible algorithms for minimizing convex functions, and that for general functions, global minimization is a difficult (NP-hard) problem. It is reasonable to ask whether there exists a class of functions that is larger than the class of all convex functions for which we can still solve the corresponding minimization problems feasibly. In this paper, we prove, in esse...

In this research paper, the problem of minimization of quadratic forms associated with the dynamics of Hopfield-Amari neural network is considered. An elegant (and short) proof of the states at which local/global minima of quadratic form are attained is provided. A theorem associated with local/global minimization of quadratic energy function using the HopfieldAmari neural network is discussed....

Learning new representations in machine learning is often tackled using a factorization of the data. For many such problems, including sparse coding and matrix completion, learning these factorizations can be difficult, in terms of efficiency and to guarantee that the solution is a global minimum. Recently, a general class of objectives have been introduced, called induced regularized factor mo...

The minimization of a functional composed of a non-smooth and non-additive regularization term and a combined L1 and L2 data-fidelity term is proposed. It is shown analytically and numerically that the new model has noticeable advantages over popular models in image processing tasks. For the numerical minimization of the new objective, subspace correction methods are introduced which guarantee ...