An Implicit Enumeration Algorithm for Quadratic Integer Programming

We present an implicit enumeration algorithm for a nonseparable quadratic integer programming problem. We utilize fathoming criteria derived from Lemke's complementary pivot algorithm, and compare the use of pseudo-costs versus generalized penalties as a guide to branching. Computational experience is provided.

[1]  A. Stuart,et al.  Portfolio Selection: Efficient Diversification of Investments , 1959 .

[2]  J. Lintner.  THE VALUATION OF RISK ASSETS AND THE SELECTION OF RISKY INVESTMENTS IN STOCK PORTFOLIOS AND CAPITAL BUDGETS , 1965 .

[3]  H. Weingartner.  Capital Budgeting of Interrelated Projects: Survey and Synthesis , 1966 .

[4]  A. M. Geoffrion.  Integer Programming by Implicit Enumeration and Balas’ Method , 1967 .

[5]  D. Luenberger.  Optimization by Vector Space Methods , 1968 .

[6]  James C. T. Mao,et al.  An Extension of Lawler and Bell's Method of Discrete Optimization with Examples from Capital Budgeting , 1968 .

[7]  G. Nemhauser,et al.  Discrete Dynamic Programming and Capital Allocation , 1969 .

[8]  Richard H. Bernhard.  Mathematical Programming Models for Capital Budgeting—A Survey, Generalization, and Critique , 1969 .

[9]  D. J. Laughhunn.  Quadratic Binary Programming with Application to Capital-Budgeting Problems , 1970, Oper. Res..

[10]  G. Ribiere,et al.  Experiments in mixed-integer linear programming , 1971, Math. Program..

[11]  Dan J. Laughhunn,et al.  Capital Expenditure Programming and Some Alternative Approaches to Risk , 1971 .

[12]  Hamdy A. Taha,et al.  A Balasian-Based Algorithm for Zero-One Polynomial Programming , 1972 .

[13]  A. M. Geoffrion,et al.  Integer Programming Algorithms: A Framework and State-of-the-Art Survey , 1972 .

[14]  Fred W. Glover,et al.  Further Reduction of Zero-One Polynomial Programming Problems to Zero-One linear Programming Problems , 1973, Oper. Res..

[15]  F. Glover.  IMPROVED LINEAR INTEGER PROGRAMMING FORMULATIONS OF NONLINEAR INTEGER PROBLEMS , 1975 .

[16]  Richard D. McBride,et al.  The factorization approach to large-scale linear programming , 1976, Math. Program..

[17]  Jean-Michel Gauthier,et al.  Experiments in mixed-integer linear programming using pseudo-costs , 1977, Math. Program..

[18]  Richard D. McBride.  A Spike Collective Dynamic Factorization Algorithm for the Simplex Method , 1978 .

[19]  R. Sargent,et al.  An efficient implementation of the Lemke algorithm and its extension to deal with upper and lower bounds , 1978 .

[20]  J. Tomlin.  Robust implementation of Lemke's method for the linear complementarity problem , 1978 .

[21]  Daniel Granot,et al.  Generalized Covering Relaxation for 0-1 Programs. , 1978 .

[22]  Jonathan S. Yormark,et al.  Optimal Real Estate Portfolios , 1979 .

[23]  P. Hansen.  Methods of Nonlinear 0-1 Programming , 1979 .

[24]  Richard D. McBride,et al.  Finding All Solutions for a Class of Parametric Quadratic Integer Programming Problems , 1980 .