We construct a convex set A with cardinality 2n and the property that an element of difference $$A-A$$ can be represented in n different ways. also show this construction is optimal by proving for any A, maximum possible number representations have $$\lfloor |A|/2 \rfloor$$ .

This paper extends the Log-robust portfolio management approach to the case with short sales, i.e., the case where the manager can sell shares he does not yet own. We model the continuously compounded rates of return, which have been established in the literature as the true drivers of uncertainty, as uncertain parameters belonging to polyhedral uncertainty sets, and maximize the worst-case por...

A general way of representing incomplete information is to use closed and convex sets of probability distributions, which are also called credal sets. Each credal set is associated with uncertainty, whose amount is quantified by an appropriate uncertainty measure. One of the requisite properties of uncertainty measures is the property of additivity, which is associated with the concept of indep...

A procedure based on convex optimization techniques for deriving normbounded uncertainty models for MIMO systems is presented. The procedure is developed for unstructured additive uncertainty models, but in principle this is no limitation since any uncertainty model of LFT type can be transformed into such a model. The models are determined by matching to process data available in the form of f...

This paper introduces the paradigm of optimization under uncertainty for modelling and solving matrix nearness problems. In particular, it considers the concrete problem of recovering correlation matrices from uncertain observations by introducing two different approaches to tackling uncertainty. The first approach invokes the framework of robust optimization to construct low error solutions th...