In this paper we present necessary conditions for global optimality for polynomial problems with box or bivalent constraints using separable polynomial relaxations. We achieve this by first deriving a numerically checkable characterization of global optimality for separable polynomial problems...

Modern sampling designs in survey statistics, in general, are constructed in order to optimize the accuracy of estimators such as totals, means and proportions. In stratified random sampling a variance minimal solution was introduced by Neyman and Tschuprov. However, practical constraints may...

In this paper we present sufficient conditions for global optimality of non-convex quadratic programs involving linear matrix inequality (LMI) constraints. Our approach makes use of the concept of a quadratic subgradient. We develop optimality conditions for quadratic programs with LMI...

Geometric branch-and-bound techniques are well-known solution algorithms for non-convex continuous global optimization problems with box constraints. Several approaches can be found in the literature differing mainly in the bounds used.

In this paper we consider the Project Scheduling Problem with resource constraints, where the objective is to minimize the project makespan. We present a new 0-1 linear programming formulation of the problem that requires an exponential number of variables, corresponding to all feasible subsets...

The paper describes an algorithm for the generation of a general class of precedence- and resource-constrained scheduling problems. Easy and hard instances for the single- and multi-mode resource-constrained project scheduling problem are benchmarked by using the state of the art...