The main contents of this paper is two-fold. First, we present a method to approximate multivariate convex functions by piecewise linear upper and lower bounds. We consider a method that is based on function evaluations only. However, to use this method, the data have to be convex....

Polynomials, trigonometric polynomials, and rational functions are widely used for the discrete approximation of functions or simulation models. Often, it is known beforehand, that the underlying unknown function has certain properties, e.g., nonnegative or increasing on a certain region....

When a disaster strikes an area, often international assistance is requested to help responding to and recovering from the disaster. The response is often characterized by the dispatch of relief items to the affected regions via depots from Humanitarian Logistics Service Providers (HLSPs). One...

In the field of the Design and Analysis of Computer Experiments (DACE) meta-models are used to approximate time-consuming simulations. These simulations often contain simulation-model errors in the output variables. In the construction of meta-models, these errors are often ignored....

In this paper, piecewise linear upper and lower bounds for univariate convex functions are derived that are only based on function value information. These upper and lower bounds can be used to approximate univariate convex functions. Furthermore, new Sandwich algorithms are proposed, that...

In the literature, methods for the construction of piecewise linear upper and lower bounds for the approximation of univariate convex functions have been proposed. We study the effect of the use of increasing convex or increasing concave transformations on the approximation of univariate...

This paper advocates the use of methods based on global approximation models for optimization problems with time-consuming function evaluations and integer variables.We show that methods based on local approximations may lead to the integer rounding of the optimal solution of the continuous...

The UN World Food Programme (WFP) is the largest humanitarian agency fighting hunger worldwide, reaching around 80 million people with food assistance in 75 countries each year. To deal with the operational complexities inherent to its mandate, WFP has been developing tools to assist their...

Our contribution is twofold. Firstly, for a system of uncertain linear equations where the uncertainties are column-wise and reside in general convex sets, we show that the intersection of the set of possible solutions and any orthant is convex.We derive a convex representation of this...

In this paper we propose a methodology for constructing decision rules for integer and continuous decision variables in multiperiod robust linear optimization problems. This type of problems finds application in, for example, inventory management, lot sizing, and manpower management. We show...