hypercube. Karmarkar isolates a subclass of such problems for which the set
of optimal solutions is connected. He suggests that this approach will solve
a large class of 0-1 integer programs not previously considered tractable,
including many set covering problems. J. Mitchell and M. Todd study per-
fect matching problems, which are a class of integer programs known to be
solvable in polynomial time. They describe a cutting plane method for such
problems that uses interior-point methods to solve linear programming re-
laxations of the problem and present computational data. Finally, the paper
of S. Abhyankar, T. Morin, and T. Trafalis outlines two methods for solving
multi-objective linear programs, including an interior-point method to find a
single efficient solution, and a method of circumscribed algebraic sets to find
the entire set of efficient solutions.
We would like to take this opportunity to thank the anonymous referees.
We also thank the National Science Foundation and Office of Naval Research
for their support of the conference. The breadth of topics covered owed much
to the valuable advice of the organizing committee, consisting of Victor Klee
and Steve Smale. Finally, the success of the meeting owed much to the
excellent local arrangements and support of the AMS staff, in particular Ms.
The papers in this volume are in final form and no version will be submit-
ted for publication elsewhere, except for the paper by I ~ i n J. Lustig and the
paper by John E. Mitchell and Michael J. Todd.
Jeffrey C. Lagarias
Michael J. Todd