We examine a heterogeneous alternating-direction method for the approximate solution of the FENE Fokker–Planck equation from polymer fluid dynamics and we use this method to solve a coupled (macro-micro) Navier–Stokes–Fokker–Planck system for dilute polymeric fluids. In this context the Fokker–Planck equation is posed on a high-dimensional domain and is therefore challenging from a computationa...

Traditional decomposition based branch-and-bound algorithms, like branch-and-price, can be very e cient if the duality gap is not too large. However, if this is not the case, the branchand-bound tree may grow rapidly, preventing the method to nd a good solution. In this paper, we present a new decompositon algorithm, called ADGO (Alternating Direction Global Optimization algorithm), for globall...

We present a closed-form solution for convex Nonlinear Programming (NLP). It is closed-form solution if all the constraints are linear, quadratic, or homogeneous. It is polynomial when applied to convex NLP. It gives exact optimal solution when applied to LP. The T-forward method moves forward inside the feasible region with a T-shape path toward the increasing direction of the objective functi...

Branching in mixed-integer (or integer) linear programming requires choosing both the branching variable and the branching direction. This paper develops a number of new methods for making those two decisions either independently or together with the goal of reaching the first integer-feasible solution quickly. These new methods are based on estimating the probability of satisfying a constraint...

The fundamental idea behind all multigrid methods is to compute using diierent scales in order to obliterate error components of diierent scales. Error components can be thought of as waves. A long wave, which has low frequency, on one grid is a short wave, or high frequency, on a coarse enough related grid. A number of iterative methods (e.g., relaxation and alternating direction implicit meth...

We consider the problem of whether a given geometry can be molded in a two part, rigid, reusable mold with opposite removal directions. We describe an efficient algorithm for solving the opposite direction moldability problem for a 2D “polygon” bounded by edges that may be either straight or curved. We introduce a structure, the normal graph of the polygon, that represents the range of normals ...

In this study we proposed two Quasi-Newton methods to deal with traffic assignment in the capacitated network. The methods combine Newton formula, column generation and penalty techniques. The first method employ the gradient of the objective function to obtain an improving feasible direction scaled by the second-order derivatives. The second one is to employ Rosen gradient to obtain an improvi...

Wurtzite AlN is widely used for deep ultraviolet optoelectronic devices (DUV), which are generally grown along the [0001]-direction of the wurtzite structure on currently available substrates. However, huge internal electrostatic fields are presented within the material along [0001] axis induced by piezoelectric and spontaneous polarization, which has limited the internal quantum efficiency of ...

We propose a new method for practical non-Gaussian and nonstationary underwater noise modeling. This model is very useful for passive sonar in shallow waters. In this application, measurement of additive noise in natural environment and exhibits shows that noise can sometimes be significantly non-Gaussian and a time-varying feature especially in the variance. Therefore, signal processing algori...