Uniqueness of integer solution of linear equations

Optimization Letters

Volumn 4, Issue 4, 2010, Pages 559-565

  Mangasarian, O L ^a,b   Ferris, M C ^a  

^a University of Wisconsin   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Absolute value equations; Integer solution uniqueness; Linear equations; Linear programming

Indexed keywords

ABSOLUTE VALUE EQUATIONS; DIAGONAL MATRICES; DUAL CONES; INTEGER SOLUTIONS; INTEGER VARIABLES; LINEAR PROGRAMS; PROGRAMMING SOLUTIONS; SUFFICIENT CONDITIONS;

INTEGER PROGRAMMING; LINEAR PROGRAMMING; OPTIMIZATION;

LINEAR EQUATIONS;

EID: 77956871079     PISSN: 18624472     EISSN: 18624480     Source Type: Journal    
DOI: 10.1007/s11590-010-0183-0     Document Type: Article

References (12)

1. Balas E., Zemel E.: An algorithm for large zero-one knapsack problems. Oper. Res. 28, 1132-1154 (1980).
2. Fayard D., Plateau G.: An algorithm for the solution of the 0-1 knapsack problem. Computing 28, 269-287 (1982).
3. Horst R., Pardalos P., Thoai N. V.: Introduction to Global Optimization. Kluwer, Dodrecht (1995).
4. ILOG, Incline Village, Nevada. ILOG CPLEX 9. 0 User's Manual (2003). http://www. ilog. com/products/cplex/.
5. Mangasarian O. L.: Uniqueness of solution in linear programming. Linear Algebra Appl. 25, 151-162 (1979).
6. Mangasarian, O. L.: Knapsack feasibility as an absolute value equation solvable by successive linear programming. Optim. Lett. 3, 161-170 (2009). ftp://ftp. cs. wisc. edu/pub/dmi/tech-reports/08-03. pdf. Optimization Letters online version: http://www. springerlink. com/content/7011287432285747/.
7. Mangasarian, O. L., Recht, B.: Probability of unique integer solution to a system of linear equations. Technical Report 09-02, Data Mining Institute, Computer Sciences Department, University of Wisconsin, Madison, Wisconsin, September 2009. ftp://ftp. cs. wisc. edu/pub/dmi/tech-reports/09-02. pdf.
8. MATLAB. User's Guide. The MathWorks, Inc., Natick (1994-2006). http://www. mathworks. com.
9. Motzkin, T. S.: Beiträge zur Theorie der Linearen Ungleichungen. Inaugural Dissertation, Jerusalem (1936).
10. Papadimitriou, C. H.: On the complexity of unique solution. In: Proceedings of the 23rd Annual Symposium on Foundations of Computer Science, pp. 14-20. IEEE CNF, Chicago (1982).
11. Prokopyev O. A., Huang H.-X., Pardalos P. M.: On complexity of unconstrained hyperbolic 0-1 programming problems. Oper. Res. Lett. 33, 312-318 (2005).
12. Valiant, L. G., Vazirani, V. V.: Np is as easy as detecting unique solutions. In: Annual ACM Symposium on Theory of Computing, Proceedings of the 17th Annual ACM Symposium on Theory of Computing, pp. 458-463. Association for Computing Machinery, New York (1985).