Graph partitioning and continuous quadratic programming

A continuous quadratic programming formulation is given for min-cut graph p artitioning problems. In these problems, we partition the vertices of a gra ph into a collection of disjoint sets satisfying specified size constraints , while minimizing the sum of weights of edges connecting vertices in diffe rent sets. An optimal solution is related to an eigenvector (Fiedler vector ) corresponding to the second smallest eigenvalue of the graph's Laplacian. Necessary and sufficient conditions characterizing local minima of the qua dratic program are given. The effect of diagonal perturbations on the numbe r of local minimizers is investigated using a test problem from the literat ure.