An Inventory-Location Model: Formulation, Solution Algorithm and Computational Results

We introduce a new distribution center (DC) location model that incorporates working inventory and safety stock inventory costs at the distribution centers. In addition, the model incorporates transport costs from the suppliers to the DCs that explicitly reflect economies of scale through the use of a fixed cost term. The model is formulated as a … Read more

A Computational Study of a Gradient-Based Log-Barrier Algorithm for a Class of Large-Scale SDPs

The authors of this paper recently introduced a transformation \cite{BuMoZh99-1} that converts a class of semidefinite programs (SDPs) into nonlinear optimization problems free of matrix-valued constraints and variables. This transformation enables the application of nonlinear optimization techniques to the solution of certain SDPs that are too large for conventional interior-point methods to handle efficiently. Based … Read more

Variational Analysis of the Abscissa Mapping for Polynomials

The abscissa mapping on the affine variety $M_n$ of monic polynomials of degree $n$ is the mapping that takes a monic polynomial to the maximum of the real parts of its roots. This mapping plays a central role in the stability theory of matrices and dynamical systems. It is well known that the abscissa mapping … Read more

Variational Analysis of Non-Lipschitz Spectral Functions

We consider spectral functions $f \circ \lambda$, where $f$ is any permutation-invariant mapping from $\Cx^n$ to $\Rl$, and $\lambda$ is the eigenvalue map from the set of $n \times n$ complex matrices to $\Cx^n$, ordering the eigenvalues lexicographically. For example, if $f$ is the function “maximum real part Citation Math. Programming 90 (2001), pp. 317-352

Automatic Differentiation Tools in Optimization Software

We discuss the role of automatic differentiation tools in optimization software. We emphasize issues that are important to large-scale optimization and that have proved useful in the installation of nonlinear solvers in the NEOS Server. Our discussion centers on the computation of the gradient and Hessian matrix for partially separable functions and shows that the … Read more

Properties of the Log-Barrier Function on Degenerate Nonlinear Programs

We examine the sequence of local minimizers of the log-barrier function for a nonlinear program near a solution at which second-order sufficient conditions and the Mangasarian-Fromovitz constraint qualifications are satisfied, but the active constraint gradients are not necessarily linearly independent. When a strict complementarity condition is satisfied, we show uniqueness of the local minimizer of … Read more