The problem of sample allocation in multipurpose surveys is complicated by the fact that an efficient allocation for some estimates may be inefficient for others. There may also be precision goals that must be met for certain estimates plus constraints on costs and minimum sample sizes for strata to permit variance estimation. These requirements lead to formulating the allocation problem as one...

Extended mathematical programs are collections of functions and variables joined together using specific optimization and complementarity primitives. This paper outlines a mechanism to describe such an extended mathematical program by means of annotating the existing relationships within a model to facilitate higher level structure identification. The structures, which often involve constraints...

We describe in this work a number of central problems of machine learning and show how they can be modeled and solved as mathematical programs of various complexity.

In general terms some situations are described which require the exploitation of heuristics either to solve a mathematical optimization problem or to analyse results. A possibility to implement heuristic knowledge for selecting a suitable algorithm depending on available problem data and information retrieved from the user, is investigated in detail. We describe some inference strategies and kn...

We propose a mathematical programming method to deal with uncertainty in the observations of a classification problem. This means that we can deal with situations where instead of a sample (xi, yi) we may only have a distribution over (xi, yi) at our disposition. In particular, we derive a robust formulation when the uncertainty is given by a normal distribution. This leads to Second Order Cone...

Whenever we base some decision on a comparison of numerical values, we must consider the impurity of those values. Thus, if a decision depends on whether v = 0, we instead test if |v| ≤ τ , where τ is some small value called a tolerance. More generally, for a particular comparison of the form v = V , we define two tolerances: absolute and relative, denoted τa and τr, respectively. Then, we test...

Given a set of entities, Cluster Analysis aims at finding subsets, called clusters, which are homogeneous and/or well separated. As many types of clustering and criteria for homogeneity or separation are of interest, this is a vast field. A survey is given from a mathematical programming viewpoint. Steps of a clustering study, types of clustering and criteria are discussed. Then algorithms for ...

November 20, 2009. Along with so many colleagues, I am deeply saddened by the news of Paul Tseng’s disappearance while on a kayak trip on the Jinsha River in China on August 13, 2009. Many of us have many wonderful memories of times spent with Paul – visits, collaborations, conversations, conference social events – and many have been influenced by his scholarly, incisive, and prolific research....

We discuss the application of the Haskell/Gofer type classes and constructor classes to the implementation and teaching of the manipulation techniques in the domain of formal mathematical expressions. We show also how the lazy evaluation paradigms simplify the construction and the presentation of several algorithms dealing with iterative data types, such as power series or formal Pad e expansio...