Several new observations which lead to new correctness proofs of two known algorithms (Hu-Tucker and Garsia-Wachs) for construction of optimal alphabetic trees are presented. A generalized version of the Garsia-Wachs algorithm is given. Proof of this generalized version works in a structured and illustrative way and clariies the usually poorly-understood behavior of both the Hu-Tucker and Garsi...

Tucker decomposition is a standard method for processing multi-way (tensor) measurements and finds many applications in machine learning data mining, among other fields. When tensor arrive streaming fashion or are too to jointly decompose, incremental analysis preferred. In addition, dynamic adaptation of bases desired when the nominal subspaces change. At same time, it has been documented that...

A tribute for Tucker Childs

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...