Bintong Chen

A non-interior-point continuation method for linear complementarity problems

This paper presents a continuation method for linear complementarily problems based on a new smooth equation formulation. In particular, the case of a linear complementarity problem defined by a positive semidefinite or

Smooth Approximations to Nonlinear Complementarity Problems

P_0

A Global Linear and Local Quadratic Noninterior Continuation Method for Nonlinear Complementarity Problems Based on Chen--Mangasarian Smoothing Functions

matrix is studied in detail. Extensive numerical testing of the continuation method is performed for both problems in the literature and randomly generated problems.

Optimal pacing of trains in freight railroads: model formulation and solution

It is well known that a nonlinear complementarity problem (NCP) can be formulated as a system of nonsmooth equations. Chen and Mangasarian [Comput. Optim. Appl., 5 (1996), pp. 97--138] proposed a class of parametric smooth functions by twice integrating a probability density function. As a result, the nonsmooth equations can be approximated by smooth equations. This paper refines the smooth functions proposed by Chen and Mangasarian and investigates their structural properties. The refinement allows us to establish the existence, uniqueness, and limiting properties of the trajectory defined by the solutions of these smooth equation approximations. In addition, global error bounds for the NCP with a uniform P-function are obtained.

A PENALIZED FISCHER-BURMEISTER NCP-FUNCTION

A noninterior continuation method is proposed for nonlinear complementarity problems. It improves the noninterior continuation methods recently studied by Burke and Xu [Math. Oper. Res., 23 (1998), pp. 719--734] and Xu [The Global Linear Convergence of an Infeasible Non-Interior Path-following Algorithm for Complementarity Problems with Uniform P-functions, Preprint, Department of Mathematics, University of Washington, Seattle, 1996]; the interior point neighborhood technique is extended to a broader class of smoothing functions introduced by Chen and Mangasarian [Comput. Optim. Appl., 5 (1996), pp. 97--138]. The method is shown to be globally linearly convergent following the methodology established by Burke and Xu. In addition, a local acceleration step is added to the method so that it is also locally quadratically convergent under suitable assumptions.

Expected Value of Distribution Information for the Newsvendor Problem

Recent developments in location systems technology for railroads provide a train dispatcher with the capability to improve the operations of a rail line by pacing trains over a territory; i.e., to permit trains to travel at less than maximum velocity to minimize fuel consumption while maintaining a given level of performance. Traditional railroad dispatching models assume that the velocities of the trains moving over a dispatchers territory are fixed at their maximum value and, thus, are incapable of dealing with a pacing situation. This paper presents a mathematical programming model for the pacing problem and describes alternative solution procedures for this model. Analytical and numerical evidence are presented that confirm the applicability of a heuristic solution procedure for this problem, as well as providing evidence that a pacing approach versus the traditional dispatching approach is an efficient and potentially cost effective method for the control of train movements.

A Global and Local Superlinear Continuation-Smoothing Method for P 0 and R 0 NCP or Monotone NCP

Abstract.We introduce a new NCP-function in order to reformulate the nonlinear complementarity problem as a nonsmooth system of equations. This new NCP-function turns out to have stronger theoretical properties than the widely used Fischer-Burmeister function and other NCP-functions suggested previously. Moreover, numerical experience indicates that a semismooth Newton method based on this new NCP-function performs considerably better than the corresponding method based on the Fischer-Burmeister function.

TWO MOMENTS ESTIMATION OF THE DELAY ON SINGLE-TRACK RAIL LINES WITH SCHEDULED TRAFFIC

This paper extends previous work on the distribution-free newsvendor problem, where only partial information about the demand distribution is available. More specifically, the analysis assumes that the demand distribution f belongs to a class of probability distribution functions (pdf) F with mean μ and standard deviation σ. While previous work has examined the expected value of distribution information (EVDI) for a particular order quantity and a particular pdf f, this paper aims at computing the maximum EVDI over all f ∈ F for any order quantity. In addition, an optimization procedure is provided to calculate the order quantity that minimizes the maximum EVDI.

Job sequencing and due date assignment in a single machine shop with uncertain processing times

We propose a continuation method for a class of nonlinear complementarity problems (NCPs), including the NCP with a P0 and R0 function and the monotone NCP with a feasible interior point. The continuation method is based on a class of Chen--Mangasarian smoothing functions. Unlike many existing continuation methods, the method follows noninterior smoothing paths, and, as a result, initial points can be easily constructed. In addition, we introduce a procedure to dynamically update the neighborhoods associated with the smoothing paths, so that the algorithm is both globally convergent and locally superlinearly convergent under suitable assumptions. Finally, a hybrid continuation-smoothing method is proposed and is shown to have the same convergence properties under weaker conditions.

Optimal scheduling of interactive and noninteractive traffic in telecommunication systems

A substantial literature exists on the estimation of the delay function for a single-track railroad with the assumption that the trains are uniformly distributed over time. In order to make the estimation more accurate and realistic, this paper provides the definition of delay functions for a scheduled railroad in which each train has a scheduled departure and arrival time. The key feature of this paper is that the uncertainty in the actual train departure time is explicitly taken into consideration. Since the variance of delay is important in the measurement of the reliability of a given set of schedules, both the mean and the variance of delay are estimated by solving a system of nonlinear equations.