A bundle-filter method for nonsmooth convex constrained optimization

Mathematical Programming

Volumn 116, Issue 1-2, 2009, Pages 297-320

  Karas, Elizabeth ^a   Ribeiro, Ademir ^a   Sagastizábal, Claudia ^b   Solodov, Mikhail ^b  

^a FEDERAL UNIVERSITY OF PARANÁ   (Brazil)

^b IMPA   (Brazil)

Author keywords

Bundle methods; Constrained optimization; Filter methods; Nonsmooth convex optimization

Indexed keywords

AEROSPACE APPLICATIONS; ALGORITHMS; BOOLEAN FUNCTIONS; CONSTRAINT THEORY; EVOLUTIONARY ALGORITHMS; INTEGER PROGRAMMING; MATHEMATICAL PROGRAMMING; NONLINEAR PROGRAMMING; OPTIMIZATION; QUADRATIC PROGRAMMING; SCHEDULING ALGORITHMS; VARIATIONAL TECHNIQUES; WAVE FILTERS;

(I ,J) CONDITIONS; (N-1) CRITERION; BUNDLE METHODS; COMPUTATIONAL RESULTS; CONSTRAINED OPTIMIZATION PROBLEMS; CONVEX OPTIMIZATION; FILTER METHODS; FILTER STRATEGY; NONSMOOTH; SPRINGER (CO); SUB-PROBLEMS; VARIATIONAL INEQUALITIES;

CONSTRAINED OPTIMIZATION;

EID: 45749105960     PISSN: 00255610     EISSN: 14364646     Source Type: Journal    
DOI: 10.1007/s10107-007-0123-7     Document Type: Article

References (30)

1. Auslender A. (1987). Numerical methods for nondifferentiable convex optimization. Math. Program. Study 30: 102-126
2. Auslender A. (1997). How to deal with the unbounded in optimization: theory and algorithms. Math. Program. 79: 3-18
3. Bonnans J.F., Gilbert J.-Ch., Lemaréchal C. and Sagastizábal C. (2003). Numerical Optimization. Theoretical and Practical Aspects. Universitext. Springer, Berlin
4. Fletcher R., Gould N., Leyffer S., Toint P. and Wächter A. (2002). Global convergence of trust-region and SQP-filter algorithms for general nonlinear programming. SIAM J. Optim. 13: 635-659
5. Fletcher, R., Leyffer, S.: A bundle filter method for nonsmooth nonlinear optimization. Numerical Analysis Report NA/195. Department of Mathematics, The University of Dundee, Scotland (1999)
6. Fletcher R. and Leyffer S. (2002). Nonlinear programming without a penalty function. Math. Program 91: 239-269
7. Fletcher R., Leyffer S. and Toint P.L. (2002). On the global convergence of a filter-SQP algorithm. SIAM J. Optim. 13: 44-59
8. Frangioni A. (1996). Solving semidefinite quadratic problems within nonsmooth optimization algorithms. Comput. Oper. Res. 23: 1099-1118
9. Frangioni A. (2002). Generalized bundle methods. SIAM J. Optim. 13: 117-156
10. Gonzaga C.C., Karas E.W. and Vanti M. (2003). A globally convergent filter method for nonlinear programming. SIAM J. Optim. 14: 646-669
11. Hiriart-Urruty J.-B. and Lemaréchal C. (1993). Convex Analysis and Minimization Algorithms. Number 305-306 in Grund. der Math. Wiss. Springer, Heidelberg
12. Hock W. and Schittkowski K. (1981). Test Examples for Nonlinear Programming Codes. Lecture Notes in Economics and Mathematical Systems, vol. 187. Springer, Berlin
13. Kiwiel K.C. (1985). Methods of Descent for Nondifferentiable Optimization. Lecture Notes in Mathematics, vol. 1133. Springer, Berlin
14. Kiwiel K.C. (1985). An exact penalty function algorithm for nonsmooth convex constrained minimization problems. IMA J. Numer. Anal. 5: 111-119
15. Kiwiel K.C. (1986). A method for solving certain quadratic programming problems arising in nonsmooth optimization. IMA J. Numer. Anal. 6: 137-152
16. Kiwiel K.C. (1987). A constraint linearization method for nondifferentiable convex minimization. Numer. Math. 51: 395-414
17. Kiwiel K.C. (1991). Exact penalty functions in proximal bundle methods for constrained convex nondifferentiable minimization. Math. Program. 52: 285-302
18. Lemaréchal C., Nemirovskii A. and Nesterov Yu. (1995). New variants of bundle methods. Math. Program. 69: 111-148
19. Lemaréchal C. and Sagastizábal C. (1997). Variable metric bundle methods: from conceptual to implementable forms. Math Program 76: 393-410
20. Lukšan L (1984). Dual method for solving a special problem of quadratic programming as a subproblem at linearly constrained nonlinear minimax approximation. Kybernetika 20: 445-457
21. Lukšan, L., Vlček, J.: A bundle-Newton method for nonsmooth unconstrained minimization. Math. Program. 83(3, Ser. A):373-391 (1998)
22. Lukšan L. and Vlček J. (1999). Globally convergent variable metric method for convex nonsmooth unconstrained minimization. J. Optim. Theory Appl. 102(3): 593-613
23. Lukšan, L., Vlček, J.: NDA: Algorithms for nondifferentiable optimization. Research Report V-797. Institute of Computer Science, Academy of Sciences of the Czech Republic, Prague (2000)
24. Lukšan L. and Vlček J. (2001). Algorithm 811, NDA, http://www.netlib.org/toms/811. ACM Trans. Math. Softw. 27(2): 193-213
25. Mangasarian O.L. (1969). Nonlinear Programming. McGraw-Hill, New York
26. Mifflin R. (1977). An algorithm for constrained optimization with semismooth functions. Math. Oper. Res. 2: 191-207
27. Mifflin R. (1982). A modification and extension of Lemarechal's algorithm for nonsmooth minimization. Math. Program. Study 17: 77-90
28. Powell M.J.D. (1985). On the quadratic programming algorithm of Goldfarb and Idnani. Math. Program. Study 25: 46-61
29. Rey P.A. and Sagastizábal C. (2002). Dynamical adjustment of the prox-parameter in variable metric bundle methods. Optimization 51: 423-447
30. Sagastizábal C. and Solodov M. (2005). An infeasible bundle method for nonsmooth convex constrained optimization without a penalty function or a filter. SIAM J. Optim. 16: 146-169