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We propose a finitely convergent dual descent method for the problem of minimizing a convex, possibly nondifferentiable, separable cost subject to linear constraints. The method has properties reminiscent of the Gauss-Seidel method in numerical analysis. As special cases we obtain the methods in [1] for network flow programs and the methods in [14] for linear programs. *Work supported by the Na...

Recently, global and local relaxation Runge–Kutta methods have been developed for guaranteeing the conservation, dissipation, or other solution properties general convex functionals whose dynamics are crucial an ordinary differential equation solution. These novel time integration procedures application in a wide range of problems that require dynamics-consistent stable numerical methods. The s...

We present the first top-down ansatz for constructing lattice Boltzmann methods (LBM) in d dimensions. In particular, we construct a relaxation system (RS) given scalar, linear, d-dimensional advection–diffusion equation. Subsequently, RS is linked to discrete velocity model (DVBM) on zeroth and energy shell. Algebraic characterizations of equilibrium, moment space, collision operator are carri...