Projection can be seem as a unifying concept that underlies inference in logic and consistency maintenance in constraint programming. This perspective allows one to import projection methods into both areas, resulting in deeper insight as well as faster solution methods. We show that inference in propositional logic can be achieved by Benders decomposition, an optimization method based on proje...

Techniques are developed for projecting the solutions of symmetric hyperbolic evolution systems onto the constraint submanifold (the constraint-satisfying subset of the dynamical field space). These optimal projections map a field configuration to the “nearest” configuration in the constraint submanifold, where distances between configurations are measured with the natural metric on the space o...

1. Abstract A novel strategy for handling the molding constraint for cast parts is presented. In a first step, a simple projection method for the velocity field is applied. If the optimized shape violates thickness constraints, this projection method is no longer sufficient and a general molding constraint is applied at the same time with thickness control. We apply an augmented Lagrangian meth...

We consider the solution of strongly monotone variational inequalities of the form F (x∗)′(x−x∗) ≥ 0, for all x ∈ X. We focus on special structures that lend themselves to sampling, such as when X is the intersection of a large number of sets, and/or F is an expected value or is the sum of a large number of component functions. We propose new methods that combine elements of incremental constra...

Iterative projection algorithms can be an effective method for solving image reconstruction problems with limited data by incorporating a priori information (constraints) on the image. However, these algorithms may experience convergence difficulties if the constraints are non-convex. Iterative projection algorithms are evaluated for the molecular envelope problem in x-ray crystallography where...