Proximal methods in vector optimization

SIAM Journal on Optimization

Volumn 15, Issue 4, 2005, Pages 953-970

  Bonnel, Henri ^a   Iusem, Alfredo Noel ^b   Svaiter, Benar Fux ^b  

^a UNIVERSITÉ DE LA NOUVELLE CALÉDONIE   (New Caledonia)

^b IMPA   (Brazil)

Author keywords

Inexact algorithm; Proximal point; Vector optimization

Indexed keywords

ALGORITHMS; PROBLEM SOLVING; VECTORS;

CONVEX OPTIMIZATION; INEXACT ALGORITHM; PROXIMAL POINT; VECTOR OPTIMIZATION;

OPTIMIZATION;

EID: 27844497912     PISSN: 10526234     EISSN: None     Source Type: Journal    
DOI: 10.1137/S1052623403429093     Document Type: Article

References (21)

1. H. BENKER, A. HAMEL, AND C. TAMMER, An algorithm for vectorial control approximation problems, in Multiple Criteria Decision Making, G. Fandel and T. Gal, eds., Springer, Berlin, 1997, pp. 3-12.
2. S. BOLINTINÉANU, Approximate efficiency and scalar stationarity in unbounded nonsmooth convex vector optimization problems, J. Optim. Theory Appl., 106 (2000), pp. 265-296.
3. S. BOLINTINÉANU, Vector variational principles; ε-efficiency and scalar stationarity, J. Convex Anal., 8 (2001), pp. 71-85.
4. R. S. BURACHIK, A. N. IUSEM, AND B. F. SVAITER, Enlargement of monotone operators with applications to variational inequalities, Set-Valued Anal., 5 (1997), pp. 159-180.
5. R. S. BURACHIK, S. SCHEIMBERG, AND B. F. SVAITER, Robustness of the hybrid extragradient proximal point algorithm, J. Optim. Theory Appl., 111 (2001), pp. 117-136.
6. D. BUTNARIU AND A. N. IUSEM, Totally Convex Functions for Fixed Point Computation and Infinite Dimensional Optimization, Kluwer, Dordrecht, 2000.
7. J. FLIEGE AND B. F. SVAITER, Steepest descent methods for multicriteria optimization, Math. Methods Oper. Res., 51 (2000), pp. 479-494.
8. A. GÖPFERT, H. RIAHI, C. TAMMER, AND C. ZALINESCU, Variational Methods in Partially Ordered Spaces, Springer, New York, 2003.
9. L. M. GRAÑA DRUMMOND AND A. N. IUSEM, A projected gradient method for vector optimization problems, Comput. Optim. Appl., 28 (2004), pp. 5-30.
10. L. M. GHAÑA DRUMMOND AND B. F. SVAITER, A steepest descent method for vector optimization, J. Comput. Appl. Math., 175 (2005), pp. 395-414.
11. J. JAHN, Theory of vector maximization: Various concepts of efficient solutions, in Multicriteria Decision Making. Advances in MCDM Models, Algorithms, Theory, and Applications, T. Gal, T. J. Stewart, and T. Hanne, eds., Kluwer, Boston, 1999, pp. 2-1-2-32.
12. T. D. LUC, Theory of Vector Optimization, Lecture Notes in Econom. and Math. Syst. 319, Springer, Berlin, 1989.
13. B. MARTINET, Régularisation d'inéquations variationelles par approximations succesives, Rev. Française de Inform. Recherche Opér., 2 (1970), pp. 154-159.
14. B. MARTINET, Algorithmes pour la Résolution de Problèmes d'optimisation et Minimax, Thèse d'état, Université de Grenoble, 1972.
15. K. MIETTINEN AND M. M. MÄKELÄ, Interactive bundle-based methods for non-differentiable multiobjective optimization: NIMBUS, Optimization, 34 (1995), pp. 231-246.
16. J. MOREAU, Proximité et dualité dans un espace hilbertien, Bull. Soc. Math. France, 93 (1965), pp. 273-299.
17. R. PATZ, J. SPITZNER, AND C. TAMMER, Decision support for location problems in town planning, Internat. Trans. Oper. Res., 9 (2002), pp. 261-278.
18. R. R. PHELPS, Convex Functions, Monotone Operators and Differentiability, Lecture Notes in Math. 1364, Springer, Berlin, 1988.
19. R. T. ROCKAFELLAR, A dual approach to solving nonlinear programming problems by unconstrained optimization, Math. Programming, 5 (1973), pp. 354-373.
20. R. T. ROCKAFELLAR, Monotone operators and the proximal point algorithm, SIAM J. Control Optim., 14 (1976), pp. 877-898.
21. M. V. SOLODOV AND B. F. SVAITER, An inexact hybrid extragradient-proximal point algorithm using the enlargement of a maximal monotone operator, Set-Valued Anal., 7 (1999), pp. 323-345.