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.
展开▼
