Chvátal closures for mixed integer programming problems

Chvátal introduced the idea of viewing cutting planes as a system for proving that every integral solution of a given set of linear inequalities satisfies another given linear inequality. This viewpoint has proven to be very useful in many studies of combinatorial and integer programming problems. The basic ingredient in these cutting-plane proofs is that for a polyhedronP and integral vectorw, if max(wx|x P, wx integer} =t, thenwx t is valid for all integral vectors inP. We consider the variant of this step where the requirement thatwx be integer may be replaced by the requirement that be integer for some other integral vector . The cutting-plane proofs thus obtained may be seen either as an abstraction of Gomory's mixed integer cutting-plane technique or as a proof version of a simple class of the disjunctive cutting planes studied by Balas and Jeroslow. Our main result is that for a given polyhedronP, the set of vectors that satisfy every cutting plane forP with respect to a specified subset of integer variables is again a polyhedron. This allows us to obtain a finite recursive procedure for generating the mixed integer hull of a polyhedron, analogous to the process of repeatedly taking Chvátal closures in the integer programming case. These results are illustrated with a number of examples from combinatorial optimization. Our work can be seen as a continuation of that of Nemhauser and Wolsey on mixed integer cutting planes.Supported by Sonderforschungsbereich 303 (DFG) and by NSF Grant Number ECS-8611841.Supported by NSF Grant Number ECS-8418392 and Sonderforschungsbereich 303 (DFG), Institut für Ökonometrie und Operations Research, Universität Bonn, FR Germany.     

Doubly-occupied orbital MCSCF methods

A new computational method for a previously suggested Multi-Configuration SCF molecular wave function is developed and applied to some simple molecules. The method involves the use of a single Fock-like hamiltonian matrix for all the MCSCF orbitals and does not involve orthogonality constraints or coupling operators. Application to lithium hydride shows that this method is capable of recovering a large part of the correlation energy and compares very favourably with conventional lengthy CI methods.     

Shock measurement with non-contacting fiber optic levers

The displacement, velocity, and acceleration performance limits of a non-contacting fiber optic lever vibration transducer are quantified. Performance characteristics are experimentally verified and measurements of displacement, velocity, and acceleration obtained from impacted plates are compared with those obtained by using conventional accelerometers. It is shown that all relevant transducer quantities, i.e., absolute maximum and minimum levels, dynamic range, and frequency response, lend themselves to quantification (or optimization) on a single graphic representation. The transducer is particularly useful for measuring high frequency shock parameters.