We introduce a concept of dual consistency of systems of linear inequalities with full generality. We show that a cardinality constrained polytope is represented by a certain system of linear inequalities if and only if the systems of linear inequalities associated with the cardinalities are dual consistent. Typical dual consistent systems of inequalities are those which describe polymatroids, ...

We consider maximizing a monotone submodular function under a cardinality constraint or a knapsack constraint in the streaming setting. In particular, the elements arrive sequentially and at any point of time, the algorithm has access to only a small fraction of the data stored in primary memory. We propose the following streaming algorithms taking O(ε) passes: 1. a (1 − e − ε)-approximation al...

Structural reliability and decomposition techniques have recently proved to be appropriate tools for solving robust uncertain mixed-integer linear programs using ellipsoidal uncertainty sets. In fact, its computational performance makes this type of problem to be an alternative method in terms of tractability with respect to robust problems based on cardinality constrained uncertainty sets. Thi...

Typically portfolio analysis is based on the expected utility or the mean-variance approach. Although the expected utility approach is the more general one, practitioners still appreciate the mean-variance approach. We give a common framework including both types of selection criteria as special cases by considering portfolio problems with terminal wealth constraints. Moreover, we propose a sol...