The auxiliary problem principle allows solving a given equilibrium problem (EP) through an equivalent auxiliary problem with better properties. The paper investigates two families of auxiliary EPs: the classical auxiliary problems, in which a regularizing term is added to the equilibrium bifunction, and the regularized Minty EPs. The conditions that ensure the equivalence of a … Read more
We study an adaptive partition-based approach for solving two-stage stochastic programs with fixed recourse. A partition-based formulation is a relaxation of the original stochastic program, and we study a finitely converging algorithm in which the partition is adaptively adjusted until it yields an optimal solution. A solution guided refinement strategy is developed to refine the … Read more
This work describes the application of a direct search method to the optimization of problems of real industrial interest, namely three new material science applications designed with the FactSage software. The search method is BiMADS, the biobjective version of the mesh adaptive direct search (MADS) algorithm, designed for blackbox optimization. We give a general description … Read more
In this paper we study stochastic quasi-Newton methods for nonconvex stochastic optimization, where we assume that only stochastic information of the gradients of the objective function is available via a stochastic first-order oracle (SFO). Firstly, we propose a general framework of stochastic quasi-Newton methods for solving nonconvex stochastic optimization. The proposed framework extends the classic … Read more
Coordinate descent algorithms solve optimization problems by successively performing approximate minimization along coordinate directions or coordinate hyperplanes. They have been used in applications for many years, and their popularity continues to grow because of their usefulness in data analysis, machine learning, and other areas of current interest. This paper describes the fundamentals of the coordinate … Read more
We introduce, discuss, and solve a hard practical optimization problem which we call the ship traffic control problem (STCP). Since we plan bi-directional traffic, STCP relates to, and in fact generalizes train timetabling on single-track networks. The objective of finding quickest routes motivates the integration of recent algorithmic ideas from dynamic collision-free routing of automated … Read more
We present a robust optimization approach to 0-1 linear programming with uncertain objective coefficients based on a safe tractable approximation of chance constraints, when only the first two moments and the support of the random parameters is known. We obtain nonlinear problems with only one additional (continuous) variable, for which we discuss solution techniques. The … Read more
We examine a decomposition approach to find good quality feasible solutions. In particular, we study a method to reduce the search-space by decomposing a problem into two partitions, where the second partition (i.e., the subproblem) contains the fixed solution of the first (i.e., the master). This type of approach is usually motivated by the presence … Read more
Given a short term mining plan, the task for an operational mine planner is to determine how the equipment in the mine should be used each day. That is, how crushers, loaders and trucks should be used to realise the short term plan. It is important to achieve both grade targets (by blending) and maximise … Read more
In the surface mining industry, the Equipment Selection Problem involves choosing an appropriate fleet of trucks and loaders such that the long-term mine plan can be satisfied. An important characteristic for multi-location (multi-location and multi-dumpsite) mines is that the underlying problem is a multi-commodity flow problem. The problem is therefore at least as difficult as … Read more