Sequential optimality conditions provide adequate theoretical tools to justify stopping criteria for nonlinear programming solvers. Here, nonsmooth approximate gradient projection and complementary approximate Karush-Kuhn-Tucker conditions are presented. These sequential optimality conditions are satisfied by local minimizers of optimization problems independently of the fulfillment of constrai...

There is a increasing interest in analysis of large-scale multiway data. The concept of multiway data refers to arrays of data with more than two dimensions, that is, taking the form of tensors. To analyze such data, decomposition techniques are widely used. The two most common decompositions for tensors are the Tucker model and the more restricted PARAFAC model. Both models can be viewed as ge...

The 2-D Tucker search problem is shown to be PPA-hard under many-one reductions; therefore it is complete for PPA. The same holds for k-D Tucker for all k ≥ 2. This corrects a claim in the literature that the Tucker search problem is in PPAD.

The hierarchical Tucker format is a way to decompose a high-dimensional tensor recursively into sums of products of lower-dimensional tensors. The number of degrees of freedom in such a representation is typically many orders of magnitude lower than the number of entries of the original tensor. This makes the hierarchical Tucker format a promising approach to solve ordinary differential equatio...

A binary matrix has the Consecutive Ones Property (C1P) if its columns can be ordered in such a way that all 1s on each row are consecutive. These matrices are used for DNA physical mapping and ancestral genome reconstruction in computational biology on the other hand they represents a class of convex bipartite graphs and are of interest of algorithm graph theory researchers. Tucker gave a forb...

A set of algebraic tools for microprocessors (Harman and Tucker [1995a], Harman and Tucker [1994], Fox and Harman [1996b]) are extended to accommodate superscalar processors, where instructions may be executed in parallel, or out of program order. This has implications for the representation of timing abstraction, the relationship between time at different levels of abstraction, and the concept...

In this paper, we study nonnegative tensor data and propose an orthogonal Tucker decomposition (ONTD). We discuss some properties of ONTD develop a convex relaxation algorithm the augmented Lagrangian function to solve optimization problem. The convergence is given. employ on image sets from real world applications including face recognition, representation, hyperspectral unmixing. Numerical re...

Tensor decomposition methodologies are proposed to reduce the memory requirement of translation operator tensors arising in fast multipole method-fast Fourier transform (FMM-FFT)-accelerated surface integral equation (SIE) simulators. These leverage Tucker, hierarchical Tucker (H-Tucker), and tensor train (TT) decompositions compress FFT'ed stored 3-D 4-D array formats. Extensive numerical test...