A cutting plane algorithm for the bilinear programming problem

In this paper we discuss the properties of a Bilinear Programming problem, and develop a convergent cutting plane algorithm. The cuts involve only a subset of the variables and preserve the special structure of the constraints involving the remaining variables. The cuts are deeper than other similar cuts.

[1]  R. D. Young Hypercylindrically Deduced Cuts in Zero-One Integer Programs , 1971, Oper. Res..

[2]  Fred W. Glover Convexity cuts for multiple choice problems , 1973, Discret. Math..

[3]  Raymond K. Mueller,et al.  A Method for Solving the Indefinite Quadratic Programming Problem , 1970 .

[4]  G. Owen Cutting planes for programs with disjunctive constraints , 1973 .

[5]  K. Ritter,et al.  A method for solving maximum-problems with a nonconcave quadratic objective function , 1966 .

[6]  R. Cottle,et al.  RITTER'S CUTTING PLANE METHOD FOR NONCONVEX QUADRATIC PROGRAMMING , 1969 .

[7]  Fred W. Glover,et al.  Concave Programming Applied to a Special Class of 0-1 Integer Programs , 1973, Oper. Res..

[8]  Robert J. Townsley,et al.  THE MAXIMIZATION OF A QUADRATIC FUNCTION OF VARIABLES SUBJECT TO LINEAR INEQUALITIES*t , 1964 .

[9]  A. Victor Cabot,et al.  Solving Certain Nonconvex Quadratic Minimization Problems by Ranking the Extreme Points , 1970, Oper. Res..

[10]  Egon Balas,et al.  Intersection Cuts - A New Type of Cutting Planes for Integer Programming , 1971, Oper. Res..

[11]  Fred W. Glover,et al.  Polyhedral annexation in mixed integer and combinatorial programming , 1975, Math. Program..

[12]  Fred W. Glover Polyhedral convexity cuts and negative edge extensions , 1974, Z. Oper. Research.

[13]  Arthur M. Geoffrion,et al.  Elements of Large-Scale Mathematical Programming Part I: Concepts , 1970 .

[14]  Egon Balas,et al.  Integer programming and convex analysis: Intersection cuts from outer polars , 1972, Math. Program..

[15]  Frederick S. Hillier,et al.  Introduction of Operations Research , 1967 .

[16]  Claude-Alain Burdet Polaroids: A new tool in non‐convex and in integer programming , 1973 .

[17]  E. Balas,et al.  Maximizing a Convex Quadratic Function Subject to Linear Constraints. , 1973 .

[18]  Fred W. Glover,et al.  Convexity Cuts and Cut Search , 1973, Oper. Res..