Graph implementations for nonsmooth convex programs

Lecture Notes in Control and Information Sciences

Volumn 371, Issue , 2008, Pages 95-110

  Grant, Michael C ^a   Boyd, Stephen P ^a  

^a STANFORD UNIVERSITY   (United States)

Author keywords

Conic optimization; Convex optimization; Disciplined convex programming; Nondifferentiable functions; Nonsmooth optimization; Optimization modeling languages; Second order cone programming; Semidefinite programming

Indexed keywords

LINEAR PROGRAMMING; MODELING LANGUAGES;

CONIC OPTIMIZATION; CONVEX OPTIMISATION; CONVEX PROGRAMS; DISCIPLINED CONVEX PROGRAMMING; NON-DIFFERENTIABLE FUNCTIONS; NONSMOOTH OPTIMIZATION; OPTIMIZATION MODELING LANGUAGE; OPTIMIZATION MODELS; SECOND-ORDER CONE PROGRAMMING; SEMI-DEFINITE PROGRAMMING;

SECOND-ORDER CONE PROGRAMMING;

EID: 36849072045     PISSN: 01708643     EISSN: None     Source Type: Book Series    
DOI: 10.1007/978-1-84800-155-8_7     Document Type: Article

References (20)

1. Alizadeh, F., Goldfarb, D.: Second-order cone programming (January 2004)
2. Bertsekas, D.P.: Convex Analysis and Optimization. In: Nedić, A., Ozdaglar, A.E. (eds.) Athena Scientific (2003)
3. Bland, R., Goldfarb, D., Todd, M.: The ellipsoid method: A survey. Operations Research 29(6), 1039-1091 (1981)
4. Borwein, J., Lewis, A.: Convex Analysis and Nonlinear Optimization: Theory and Examples. Springer, Heidelberg (2000)
5. Ben-Tal, A., Nemirovski, A.: Lectures on Modern Convex Optimization: Analysis, Algorithms and Engineering Applications. MPS/SIAM Series on Optimization. SIAM, Philadelphia (2001)
6. Boyd, S., Vandenberghe, L.: Convex Optimization. Cambridge Univ. Press, Cambridge (2004), http://www.stanford.edu/~boyd/cvxbook.html
7. Dantzig, G.: Linear Programming and Extensions. Princeton University Press, Princeton (1963)
8. Grant, M., Boyd, S.: CVX: MATLAB® software for disciplined convex programming, version 1.1 (September 2007), http://www.stanford.edu/~boyd/cvx/
9. Grant, M., Boyd, S., Ye, Y.: Disciplined convex programming. In: Liberti, L., Maculan, N. (eds.) Global Optimization: from Theory to Implementation, Nonconvex Optimization and Its Applications, pp. 155-210. Springer Science+Business Media, Inc., New York (2006)
10. Grant, M.: Disciplined Convex Programming. PhD thesis, Department of Electrical Engineering, Stanford University (December 2004)
11. Löfberg, J.: YALMIP: A toolbox for modeling and optimization in MATLAB®. In: Proceedings of the CACSD Conference, Taipei, Taiwan (2004), http://control.ee.ethz.ch/~joloef/yalmip/php
12. Lobo, M., Vandenberghe, L., Boyd, S., Lebret, H.: Applications of second-order cone programming. Linear Algebra and its Applications 284, 193-228 (1998) (special issue on Signals and Image Processing)
13. MOSEK ApS. Mosek (software package) (September 2007), http://www.mosek.com
14. Nesterov, Yu., Nemirovsky, A.: Interior-Point Polynomial Algorithms in Convex Programming: Theory and Algorithms of Studies in Applied Mathematics, vol. 13. SIAM Publications, Philadelphia, PA (1993)
15. Rockafellar, R.T.: Convex Analysis. Princeton University Press, Princeton (1970)
16. Sturm, J.: Using SeDuMi 1.02, a MATLAB® toolbox for optimization over symmetric cones. Optimization Methods and Software 11, 625-653 (1999), Updated version available at http://sedumi.mcmaster.ca
17. Ton, K., Todd, M., Tutuncu, R.: SDPT3 - a MATLAB® software package for semidefinite programming. Optimization Methods and Software 11, 545-581 (1999)
18. Vanderbei, R.: LOQO: An interior point code for quadratic programming. Optimization Methods and Software 11, 451-484 (1999)
19. Vandenberghe, L., Boyd, S.: Semidefinite programming. SIAM Review 38(1), 49-95 (1996)
20. van Tiel, J.: Convex Analysis. An Introductory Text. John Wiley & Sons, Chichester (1984)