IBM THOMAS J WATSON RESEARCH CENTER YORKTOWN HEIGHTS N Y
Activity and research in Nondifferentiable Optimization NDO and Discrete Optimization are described. 1 Conjugate descent methods have been extended to constrained NDO problems. 2 A robust and efficient algorithm for the minimization of an arbitrarty convex univariate function has been devised. 3 Substantial improvements have been made to subgradient optimization relaxation methods for solving large systems of linear inequalities. 4 The subadditive characterization of facets of integer programming polyhedra has been extended to a very general class of pure integer problems. 5 Work has continued on use of subadditive functions to give a satisfactory duality theory for integer programming, to provide pricing information, and eventually to solve problems. 6 The theories of blocking pairs of polyhedra and anti-blocking pairs of polyhedra have been extended, and we have characterized pairs of polyhedra which are, respectively, the blocker and anti-blocker of some unspecified third polyhedron.