Tamra Carpenter

Symmetric indefinite systems for interior point methods

AbstractWe present a unified framework for solving linear and convex quadratic programs via interior point methods. At each iteration, this method solves an indefinite system whose matrix is

Separable Quadratic Programming via a Primal-Dual Interior Point Method and its Use in a Sequential Procedure

\left[ {\begin{array}{*{20}c} { - D^{ - 2} } & {A^T } \\ A & 0 \\ \end{array} } \right]

Maximizing the transparency advantage in optical networks

instead of reducing to obtain the usualAD2AT system. This methodology affords two advantages: (1) it avoids the fill created by explicitly forming the productAD2AT whenA has dense columns; and (2) it can easily be used to solve nonseparable quadratic programs since it requires only thatD be symmetric. We also present a procedure for converting nonseparable quadratic programs to separable ones which yields computational savings when the matrix of quadratic coefficients is dense.

SONET ring sizing with genetic algorithms

In this paper, the authors explore the full utility of Mehrotra’s predictor-corrector method in the context of linear and convex quadratic programs. They describe a procedure for doing multiple corrections at each iteration and implement it within the framework of OB1. Computational results are provided for the multiple correcting procedure using several strategies for determining the number of corrections in a given iteration. The results indicate that iteration counts can be significantly reduced by allowing higher-order corrections but at the the cost of extra work per iteration. The procedure is shown to be a level-m composite Newton interior point method, where m is the number of corrections performed in an iteration.

A ring loading application of genetic algorithms

This paper extends a primal-dual interior point procedure for linear programs to the case of convex separable quadratic objectives. Included are efficient procedures for: attaining primal and dual feasibility, variable upper bounding, and free variables. A sequential procedure that invokes the quadratic solver is proposed and implemented for solving linearly constrained convex separable nonlinear programs. Computational results are provided for several large test cases from stochastic programming. The proposed methods compare favorably with MINOS, especially for the larger examples. The nonlinear programs range in size up to 8,700 constraints and 22,000 variables. INFORMS Journal on Computing , ISSN 1091-9856, was published as ORSA Journal on Computing from 1989 to 1995 under ISSN 0899-1499.

Studies of random demands on network costs

We propose an interior point method for large-scale convex quadratic programming where no assumptions are made about the sparsity structure of the quadratic coefficient matrixQ. The interior point method we describe is a doubly iterative algorithm that invokes aconjugate projected gradient procedure to obtain the search direction. The effect is thatQ appears in a conjugate direction routine rather than in a matrix factorization. By doing this, the matrices to be factored have the same nonzero structure as those in linear programming. Further, one variant of this method istheoretically convergent with onlyone matrix factorization throughout the procedure.

Node Placement and Sizing for Copper Broadband Access Networks

We enhance the potential cost savings from optical network transparency by applying connected dominating sets and impairment-aware routing, thus reducing the density of OEO nodes substantially below that obtained with more straightforward path improvement heuristics. The funding support of NIST ATP contract 70NANB8H4018 is gratefully acknowledged.

A simple approximation algorithm for two problems in circuit design

Abstract We describe an optimization problem that arises in SONET ring sizing. We compare solutions obtained by the genetic algorithm to both optimal solutions obtained by the CPLEX mixed integer program solver and heuristic solutions generated by the algorithm that is incorporated in the SONET Toolkit—a decision support system for planning SONET networks.