The problems of (bi-)proportional rounding of a nonnegative vector or matrix, resp., are written as particular separable convex integer minimization problems. Allowing any convex (separable) objective function we use the notions of vector and matrix apportionment problems. As a broader class of...

The problems of (bi-)proportional rounding of a nonnegative vector or matrix, resp., are written as particular separable convex integer minimization problems. Allowing any convex (separable) objective function we use the notions of vector and matrix apportionment problems. As a broader class of...

The basic structure of algorithms for numerical computation of optimal approximate linear regression designs is briefly summarized. First order methods are contrasted to second order methods. A first order method, also called a vertex direction method, uses a local linear approximation of the...

The Cambridge Compromise composition of the European Parliament allocates five base seats to each Member State’s citizenry, and apportions the remaining seats proportionately to population figures using the divisor method with rounding upwards and observing a 96 seat capping. The...