On Optimization over the Efficient Set in Linear Multicriteria Programming

The efficient set of a linear multicriteria programming problem can be representedby a reverse convex constraint of the form g(z) ≤ 0, where g is a concavefunction. Consequently, the problem of optimizing some real function over the efficientset belongs to an important problem class of global optimization called reverseconvex programming. Since the concave function used in the literature is only definedon some set containing the feasible set of the underlying multicriteria programmingproblem, most global optimization techniques for handling this kind of reverse convexconstraint cannot be applied. The main purpose of our article is to present amethod for overcoming this disadvantage. We construct a concave function which isfinitely defined on the whole space and can be considered as an extension of the existingfunction. Different forms of the linear multicriteria programming problem arediscussed, including the minimum maximal flow problem as an example

A decomposition method in nonconvex mixed-integer programming

We develop a finite decomposition method for solving a wide class of non-convex mixed-integer programming problems, including, e.g., mixed-integer concave minimization problems in separable form, the general quadratic integer problem, and problems arisen from the linear complementarity problem or from the fixed-charge network flow problem. The method proposed here belongs to the branch and bound approach, in which the branching procedure is the so-called 'mixed-inter polyhedral partition' actually performed by an 'integral rectangular partition', and the bound estimation is mainly performed by linear programming or linear network flow techniques, respectively. (orig.)Available from TIB Hannover: RR 1843(94-10) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman