We study homological and geometric properties of differential algebras of finite type over a base field. The main results concern rigid dualizing complexes over such algebras.

The trellis of a finite Abelian group code is locally (i.e., trellis section by trellis section) related to the trellis of the corresponding dual group code which allows to express the basic operations of the a posteriori probability (APP) decoding algorithm (defined on a single trellis section of the primal trellis) in terms of the corresponding dual trellis section. Using this local approach,...

In this paper, we present a new decomposition algorithm for solving large-scale multistage stochastic programs (MSSP) with endogenous uncertainties. Instead of dualizing all the initial non-anticipativity constraints (NACs) and removing all the conditional non-anticipativity constraints to decompose the problem into scenario subproblems, the basic idea relies on keeping a subset of NACs as expl...

By using properties of dualizing parametrization functions, Lagrangian functions and the epigraph technique, some sufficient and necessary conditions of the stable strong duality and strong total duality for a class of DC optimization problems are established.

A hypergraph F is a set family defined on vertex set V . The dual of F is the set of minimal subsetsH of V such that F∩H 6= ∅ for any F ∈ F . The computation of the dual is equivalent to many problems, such as minimal hitting set enumeration of a subset family, minimal set cover enumeration, and the enumeration of hypergraph transversals. Although many algorithms have been proposed for solving ...