Solving the integrated airline recovery problem using column-and-row generation

Airline recovery presents very large and difficult problems requiring high quality solutions within very short time limits. To improve computational performance, the complete airline recovery problem is generally formulated as a series of sequential stages. While the sequential approach greatly simplifies the complete recovery problem, there is no guarantee of global optimality or solution quality. … Read more

A Douglas-Rachford type primal-dual method for solving inclusions with mixtures of composite and parallel-sum type monotone operators

In this paper we propose two different primal-dual splitting algorithms for solving inclusions involving mixtures of composite and parallel-sum type monotone operators which rely on an inexact Douglas-Rachford splitting method, however applied in different underlying Hilbert spaces. Most importantly, the algorithms allow to process the bounded linear operators and the set-valued operators occurring in the … Read more

Mixed-Integer Nonlinear Optimization

Many optimal decision problems in scientific, engineering, and public sector applications involve both discrete decisions and nonlinear system dynamics that affect the quality of the final design or plan. These decision problems lead to mixed-integer nonlinear programming (MINLP) problems that combine the combinatorial difficulty of optimizing over discrete variable sets with the challenges of handling … Read more

MSS: MATLAB software for L-BFGS trust-region subproblems for large-scale optimization

A MATLAB implementation of the More’-Sorensen sequential (MSS) method is presented. The MSS method computes the minimizer of a quadratic function defined by a limited-memory BFGS matrix subject to a two-norm trust-region constraint. This solver is an adaptation of the More’-Sorensen direct method into an L-BFGS setting for large-scale optimization. The MSS method makes use … Read more

On bounding the bandwidth of graphs with symmetry

We derive a new lower bound for the bandwidth of a graph that is based on a new lower bound for the minimum cut problem. Our new semide finite programming relaxation of the minimum cut problem is obtained by strengthening the well-known semide nite programming relaxation for the quadratic assignment problem by fixing two vertices in the … Read more

A Primal-Dual Regularized Interior-Point Method for Semidefinite Programming

Interior-point methods in semidefinite programming (SDP) require the solution of a sequence of linear systems which are used to derive the search directions. Safeguards are typically required in order to handle rank-deficient Jacobians and free variables. We generalize the primal-dual regularization of \cite{friedlander-orban-2012} to SDP and show that it is possible to recover an optimal … Read more