This work extends the ones of Hu et al. (2008) and Bai et al. (2013) of a logical Benders approach for globally solving Linear Programs with Complementarity Constraints. By interpreting the logical Benders method as a reversed branch-and-bound method, where the whole exploration procedure starts from the leaf nodes in an enumeration tree, we provide … Read more
In this paper, we address the Unrelated Parallel Machine Scheduling Problem (UPMSP) with sequence- and machine-dependent setup times and job due-date constraints. Different uncertainties are typically involved in real-world production planning and scheduling problems. If ignored, they can lead to suboptimal or even infeasible schedules. To avoid this, we present two new robust optimization models … Read more
In this paper, we study some bounds for nonconvex quadratically constrained quadratic programs. Recently, Zamani has proposed a dual for linearly constrained quadratic programs, where Lagrange multipliers are affine functions. By using this method, we propose two types of bounds for quadratically constrained quadratic pro- grams, quadratic and cubic bounds. For quadratic bounds, we use … Read more
Many cities have to cope with annual snowfall, but are struggling to manage their snow plowing activities efficiently. Despite the fact that winter road maintenance has been the subject of many research papers over the last 3 decades, very few practical decision support systems have been developed to deal with the complex decision problems involved … Read more
Most routing decisions assume that the world is flat meaning that routing costs are modelled as a weighted sum of total distance and time spend by delivery vehicles. However, this assumption does not apply for urban logistics operations in cities with significant altitude differences. We fill a space in the VRP literature and model routing … Read more
In many cases in which one wishes to minimize a complicated or expensive function, it is convenient to employ cheap approximations, at least when the current approximation to the solution is poor. Adequate strategies for deciding the accuracy desired at each stage of optimization are crucial for the global convergence and overall efficiency of the … Read more
A displacement aggregation strategy is proposed for the curvature pairs stored in a limited-memory BFGS (a.k.a. L-BFGS) method such that the resulting (inverse) Hessian approximations are equal to those that would be derived from a full-memory BFGS method. This means that, if a sufficiently large number of pairs are stored, then an optimization algorithm employing … Read more
In machine learning, models that generalize better often generate outputs that lie on a low-dimensional manifold. Recently, several works have separately shown finite-time manifold identification by some proximal methods. In this work we provide a unified view by giving a simple condition under which any proximal method using a constant step size can achieve finite-iteration … Read more
The occurrence of unexpected aircraft maintenance tasks can produce expensive changes in an airline’s operation. When it comes to critical tasks, it might even cancel programmed flights. Despite of it, the challenge of scheduling aircraft maintenance operations under uncertainty has received limited attention in the scientific literature. We study a dynamic airline maintenance scheduling problem, … Read more
Complementarity problems are often used to compute equilibria made up of specifically coordinated solutions of different optimization problems. Specific examples are game-theoretic settings like the bimatrix game or energy market models like for electricity or natural gas. While optimization under uncertainties is rather well-developed, the field of equilibrium models represented by complementarity problems under uncertainty … Read more