Perspective relaxation of mixed integer nonlinear programs with indicator variables

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 5035 LNCS, Issue , 2008, Pages 1-16

  Günlük, Oktay ^a   Linderoth, Jeff ^b  

^a IBM T J WATSON RESEARCH CENTER   (United States)

^b University of Wisconsin Madison   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

AEROSPACE APPLICATIONS; ARCHITECTURAL DESIGN; CERIUM COMPOUNDS; COMBINATORIAL MATHEMATICS; COMBINATORIAL OPTIMIZATION; COMPUTER NETWORKS; DYNAMIC PROGRAMMING; FACILITIES; HIGHWAY BRIDGES; INDICATORS (INSTRUMENTS); INTEGER PROGRAMMING; LINEAR PROGRAMMING; MATHEMATICAL PROGRAMMING; METROPOLITAN AREA NETWORKS; NETWORK PROTOCOLS; OPTIMIZATION; QUADRATIC PROGRAMMING; SET THEORY; VARIATIONAL TECHNIQUES;

(SPM) CLASSES; ANALYTIC FUNCTIONS; COMPUTATIONAL RESULTS; CONVEX HULLS; CONVEX SETS; DECISION VARIABLE (DV); EXPLICIT CHARACTERIZATION; FACILITY LOCATIONS; HEIDELBERG (CO); INDICATOR VARIABLES; INTEGER VARIABLES; INTERNATIONAL CONFERENCES; MIXED INTEGERS; MIXED-INTEGER NONLINEAR PROGRAMS (MINLP); NETWORK DESIGNS; NON LINEAR FUNCTIONS; QUADRATIC CONSTRAINTS; SECOND-ORDER CONE PROGRAMMING (SOCP); SPRINGER (CO); UPPER AND LOWER BOUNDS;

NONLINEAR PROGRAMMING;

EID: 45749114186     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-540-68891-4_1     Document Type: Conference Paper

References (24)

1. Günlük, O., Lee, J., Weismantel, R.: MINLP strengthening for separable convex quadratic transportation-cost ufl. Technical Report RC24213 (W0703-042), IBM Research Division (March 2007)
2. Boorstyn, R., Frank, H.: Large-scale network topological optimization. IEEE Transactions on Communications 25, 29-47 (1977)
3. Perold, A.F.: Large-scale portfolio optimization. Management Science 30, 1143-1160 (1984)
4. Bienstock, D.: Computational study of a family of mixed-integer quadratic programming problems. Mathematical Programming 74, 121-140 (1996)
5. Jobst, N.J., Horniman, M.D., Lucas, C.A., Mitra, G.: Computational aspects of alternative portfolio selection models in the presence of discrete asset choice constraints. Quantitative Finance 1, 489-501 (2001)
6. Aktürk, S., Atamtürk, A., Gürel, S.: A strong conic quadratic reformulation for machine-job assignment with controllable processing times. Technical Report BCOL Research Report 07.01, Industrial Engineering & Operations Research, University of California, Berkeley (2007)
7. Stubbs, R., Mehrotra, S.: A branch-and-cut method for 0-1 mixed convex programming. Mathematical Programming 86, 515-532 (1999)
8. Balas, E., Ceria, S., Corneujols, G.: A lift-and-project cutting plane algorithm for mixed 0-1 programs. Mathematical Programming 58, 295-324 (1993)
9. Cezik, M.T., Iyengar, G.: Cuts for mixed 0-1 conic programming. Mathematical Programming 104, 179-202 (2005)
10. Gomory, R.E.: An algorithm for the mixed integer problem. Technical Report RM-2597, The RAND Corporation (1960)
11. Atamtürk, A., Narayanan, V.: Conic mixed integer rounding cuts. In: Fischetti, M., Williamson, D.P. (eds.) IPCO 2007. LNCS, vol. 4513, Springer, Heidelberg (2007)
12. Nemhauser, G., Wolsey, L.: A recursive procedure for generating all cuts for 0-1 mixed integer programs. Mathematical Programming 46, 379-390 (1990)
13. Frangioni, A., Gentile, C: Perspective cuts for a class of convex 0-1 mixed integer programs. Mathematical Programming 106, 225-236 (2006)
14. Stubbs, R.A.: Branch-and-Cut Methods for Mixed 0-1 Convex Programming. PhD thesis, Northwestern University (December 1996)
15. Sturm, J.F.: Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones. Optimization Methods and Software 11-12, 625-653 (1999)
16. Mosek: Mosek ApS (2004), http://www.mosek.com
17. Ben-Tal, A., Nemirovski, A.: Lectures on Modern Convex Optimization. SIAM, Philadelphia (2001)
18. Ceria, S., Soares, J.: Convex programming for disjunctive optimization. Mathematical Programming 86, 595-614 (1999)
19. Bonami, P., Biegler, L.T., Conn, A.R., Cornuéjols, G., Grossmann, I.E., Laird, CD., Lee, J., Lodi, A., Margot, F., Sawaya, N., Wächter, A.: An algorithmic framework for convex mixed integer nonlinear programs. Discrete Optimization (to appear)
20. Wächter, A., Biegler, L.T.: On the implementation of a primal-dual interior point filter line search algorithm for large-scale nonlinear programming. Mathematical Programming 106(1), 25-57 (2006)
21. Lee, J.: Mixed-integer nonlinear programming: Some modeling and solution issues. IBM Journal of Research & Development 51, 489-497 (2007)
22. Bertsekas, D., Gallager, R.: Data Networks. Prentice-Hall, Endlewood Cliffs (1987)
23. Borchers, B., Mitchell, J.E.: An improved branch and bound algorithm for mixed integer nonlinear programs. Computers & Operations Research 21, 359-368 (1994)
24. Orlowski, S., Pióro, M., Tomaszewski, A., Wessäly, R.: SNDlib 1.0 - survivable network design library (2007) Optimization Online Preprint, http://www.optimization-online.org/DB_FILE/2007/08/1746.pdf