An algorithm for solving large-scale nonlinear' programs with linear constraints is presented. The method combines efficient sparse-matrix techniques as in the revised simplex method with stable quasi-Newton methods for handling the nonlinearities. A general-purpose production code (MINOS) is described, along with computational experience on a wide variety of problems.

We design a linearly homomorphic encryption scheme whose security relies on the hardness of the decisional Diffie-Hellman problem. Our approach requires some special features of the underlying group. In particular, its order is unknown and it contains a subgroup in which the discrete logarithm problem is tractable. Therefore, our instantiation holds in the class group of a non maximal order of ...

Supervised Fisher Linear Discriminant Analysis (LDA) is a classical dimensionality reduction approach. LDA assumes each class has a Gaussian density and may suffer from the singularity problem when handling high-dimensional data. We in this work consider more general class densities and show that optimizing LDA criterion cannot always achieve maximum class discrimination with the geometrical ba...

In this article, the convergence of the often used iterative softthresholding algorithm for the solution of linear operator equations in infinite dimensional Hilbert spaces is analyzed in detail. As main result we show that the algorithm converges with linear rate as soon as the underlying operator satisfies the so-called finite basis injectivity property. This result quantifies the experience ...