We discuss four discrete problems, one problem for each occurrence of the word 'match' in the title of this paper. The solutions of all four problems are based on underlying matching problems.

This note establishes a new sufficient condition for the existence and uniqueness of the Alizadeh-Haebedy-Overton direction for semidefinite programming, t~) 1997 The Mathematical Programming Society, Inc. Published by Elsevier Science B.V.

In this paper we study nonlinear semidefinite programming problems. Convexity, duality and first-order optimality conditions for such problems are presented. A second-order analysis is also given. Second-order necessary and sufficient optimality conditions are derived. Finally, sensitivity analysis of such programs is discussed. © 1997 The Mathematical Programming Society, Inc. Published by Els...

The nucleon is introduced as a new allocation concept for non-negative cooperative n-person transferable utility games. The nucleon may be viewed as the multiplicative analogue of Schmeidler's nucleolus. It is shown that the nucleon of (not necessarily bipartite) matching games can be computed in polynomial time. 9 1998 The Mathematical Programming Society, Inc. Published by Elsevier Science B.V.

The Bulletin of the Belgian Mathematical Society Simon Stevin is published by The Belgian Mathematical Society, with financial support from the Universitaire Stichting van Belgie – Fondation Universitaire de Belgique and the Fonds National de la Recherche Scientifique (FNRS). It appears quarterly and is indexed and/or abstracted in Current

The concept of representing a polytope that is associated with some combinatorial optimization problem as a linear projection of a higherdimensional polyhedron has recently received increasing attention. In this paper (written for the newsletter Optima of the Mathematical Optimization Society), we provide a brief introduction to this topic and sketch some of the recent developments with respect...