An Adaptive Sampling Sequential Quadratic Programming Method for Equality Constrained Stochastic Optimization

This paper presents a methodology for using varying sample sizes in sequential quadratic programming (SQP) methods for solving equality constrained stochastic optimization problems. The first part of the paper deals with the delicate issue of dynamic sample selection in the evaluation of the gradient in conjunction with inexact solutions to the SQP subproblems. Under reasonable … Read more

A combined model for chain expansion including the possibility of locating a new facility and modification and/or closing of existing facilities

The problem of an expanding chain (it already has some facilities) in a given area is considered. It may locate a new facility, or vary (up or down) the quality of its existing facilities, or close some of them, or a combination of all those possibilities, whatever it is the best to maximize its profit, … Read more

Minimizing earliness-tardiness costs in supplier networks – A Just-in-time Truck Routing Problem

We consider a routing problem where orders are transported just-in-time from several suppliers to an original equipment manufacturer (OEM). This implies that shipments cannot be picked up before their release date when they are ready at the supplier and should be delivered as close as possible to their due date to the OEM. Every shipment … Read more

Robust planning of production routing problem in closed-loop supply chain of beverage glass bottles

Closed-loop supply chains (CLSC) integrate forward and reverse flows of products and information. This integration helps companies to manage their supply chains better as they have more control and a broader view of the whole chain. Also, companies can have economic and environmental benefits from the returned products. Despite these advantages, managing CLSCs can be … Read more

A unified scheme for scalarization in set optimization

In this work, we propose a new scheme for scalarization in set optimization studied with the Kuroiwa set appoach. First, we define an abstract scalarizing function possessing properties such as global Lipschizity, sublinearity, cone monotonicity, cone representation property, cone interior representation property and uniform positivity. Next, we use this function to define the so called … Read more

The role of rationality in integer-programming relaxations

For a finite set $X \subset \Z^d$ that can be represented as $X = Q \cap \Z^d$ for some polyhedron $Q$, we call $Q$ a relaxation of $X$ and define the relaxation complexity $\rc(X)$ of $X$ as the least number of facets among all possible relaxations $Q$ of $X$. The rational relaxation complexity $\rc_\Q(X)$ restricts … Read more

On the weakest constraint qualification for strong local minimizers

The strong local minimality of feasible points of nonlinear optimization problems is known to possess a characterization by a strengthened version of the Karush-Kuhn-Tucker conditions, as long as the Mangasarian-Fromovitz constraint qualification holds. This strengthened condition is not easy to check algorithmically since it involves the topological interior of some set. In this paper we … Read more

A Survey on Bilevel Optimization Under Uncertainty

Bilevel optimization is a very active field of applied mathematics. The main reason is that bilevel optimization problems can serve as a powerful tool for modeling hierarchical decision making processes. This ability, however, also makes the resulting problems challenging to solve—both in theory and practice. Fortunately, there have been significant algorithmic advances in the field … Read more

A Sparse Interior Point Method for Linear Programs arising in Discrete Optimal Transport

Discrete Optimal Transport problems give rise to very large linear programs (LP) with a particular structure of the constraint matrix. In this paper we present an interior point method (IPM) specialized for the LP originating from the Kantorovich Optimal Transport problem. Knowing that optimal solutions of such problems display a high degree of sparsity, we … Read more

Learning to Use Local Cuts

An essential component in modern solvers for mixed-integer (linear) programs (MIPs) is the separation of additional inequalities (cutting planes) to tighten the linear programming relaxation. Various algorithmic decisions are necessary when integrating cutting plane methods into a branch-and-bound (B&B) solver as there is always the trade-off between the efficiency of the cuts and their costs, … Read more