On a convolution operation obtained by adding level sets : classical and new results
RAIRO - Operations Research - Recherche Opérationnelle, Tome 29 (1995) no. 2, pp. 131-154.
@article{RO_1995__29_2_131_0,
     author = {Seeger, A. and Volle, M.},
     title = {On a convolution operation obtained by adding level sets : classical and new results},
     journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
     pages = {131--154},
     publisher = {EDP-Sciences},
     volume = {29},
     number = {2},
     year = {1995},
     zbl = {0835.90094},
     mrnumber = {1337887},
     language = {en},
     url = {archive.numdam.org/item/RO_1995__29_2_131_0/}
}
Seeger, A.; Volle, M. On a convolution operation obtained by adding level sets : classical and new results. RAIRO - Operations Research - Recherche Opérationnelle, Tome 29 (1995) no. 2, pp. 131-154. http://archive.numdam.org/item/RO_1995__29_2_131_0/

1. S. Abdulfattah, M. Soueycatt, Analyse epi/hypo-graphique, Séminaire d'Analyse Convexe, Montpellier, Exposé n° 13, 1991. | MR 1154513 | Zbl 0893.49015

2. H. Attouch, Variational convergence for functions and operators, Pitman, London, 1984. | MR 773850 | Zbl 0561.49012

3. H. Attouch, Analyse épigraphique, Notes de cours de D.E.A., Montpellier, 1990.

4. J. Borwein, A note on ε-subgradients and maximal monotonicity, Pacific J. Math., 1982, 103, pp. 307-314. | MR 705231 | Zbl 0525.49010

5. N. Bourbaki, Espaces vectoriels topologiques, Chap. III, IV and V, Hermann, Paris, 1955. | Zbl 0066.35301

6. A. Brondsted, R. T. Rockafellar, On the subdifferentiability of convex functions, Proceedings AMS, 16, 1965, pp. 605-611. | MR 178103 | Zbl 0141.11801

8. V. F. Dem'Yanov, L. V. Vasil'Ev, Nondifferentiable optimization, Translation Series in Mathematics and Engineering, Optimization Software, Inc., New York, 1985. | MR 816531 | Zbl 0973.49500

8. D. Dubois, H. Prade, Operations on fuzzy numbers, Int J. Systems Sci., 1978, 9, pp. 613-626. | MR 491199 | Zbl 0383.94045

9. A. Elqortobi, Inf-convolution quasi-convexe des fonctionnelles positives, Recherche Opérationnelle, 1992, 26, pp. 301-311. | EuDML 105042 | Numdam | MR 1196903 | Zbl 0783.49008

10. M. Fedrizzi, Introduction to fuzzy sets and possibility theory, In Optimization models using fuzzy sets and possibility theory, J. KACPRZYK and S. A. ORLOVSKI (Eds.), Reidel Publishing Co., pp. 13-26. | MR 917505 | Zbl 0643.94046

11. A. Hassouni, Sous-différentiels de fonctions quasi-convexes, Thèse de 3e cycle, Université Paul Sabatier, Toulouse, 1983.

12. N. Heukemes, V. H. Nguyen, J.-J. Strodiot, ε-optimal solutions in nondifferentiable programming and some related questions, Math. Programming, 1983, 25, pp. 307-365. | MR 689660 | Zbl 0495.90067

13. J.-B. Hiriart-Urruty, A. Seeger, The second-order subdifferential and the Dupin indicatrices of a nondifferentiable convex function, Proc. Math. Soc., 1989, 58, pp. 351-365. | MR 977481 | Zbl 0632.53009

14. M. Kolonko, Optimal compactification of a floorplan and its relation to other optimization problems-A dynamic programming approach, ZOR-Meth. Oper. Res., 1993, 7, pp. 75-95. | MR 1213679 | Zbl 0768.90081

15. A.G. Kusraev, S. S. Kutateladze, Subdifferential calculus, Nauka Publishing House, Novosibirsk, 1987 (in Russian). | Zbl 1137.49002

16. C. Lemarechal, J. Zowe, Some remarks on the construction of higher-order algorithms in convex optimization, Applied Mathematics and Optimization, 1983, 10, pp. 51-68. | MR 701900 | Zbl 0527.65042

17. J. E. Martinez-Legaz, On lower subdifferentiable functions. In Trends in Mathematical Optimization, K. H. HOFFMANN, J. B. HIRIART-URRUTY, C. LEMARECHAL, J. ZOWE, Eds., International Series of Numerical Mathematics, 84, Birkhàuser-Verlag, Basel, 1988, pp. 197-232. | MR 1017954 | Zbl 0643.49015

18. W. Oettli, Epsilon-solutions and epsilon-supports, Optimization, 1985, 16, pp. 491-496. | MR 791360 | Zbl 0577.90060

19. G. Passty, The parallel sum of non-linear monotone operators, Nonlinear Analysis TMA, 1986, 10, pp. 215-227. | MR 834503 | Zbl 0628.47033

20. J.-P. Penot, M. Volle, On strongly convex and paraconvex dualities, In Lecture Notes in Economies and Mathematical Systems, Springer-Verlag, 1990, 345, pp. 198-218. | MR 1117933 | Zbl 0701.49038

21. R. T. Rockafellar, Convex analysis, Princeton Univ. Press, Princeton, N. J., 1970. | Zbl 0932.90001

22. R. T. Rockafellar, Conjugate duality and optimization, In Regional Conference Series in Applied Mathematics, 1973, 16, SIAM Publications. | MR 373611 | Zbl 0296.90036

23. A. Seeger, Analyse du second ordre de problèmes non différentiables, Thèse, Université Paul Sabatier, Toulouse, 1986.

24. A. Seeger, Direct and inverse addition in convex analysis and applications, J. Math. Anal and Appl., 1990, 148, pp. 317-349. | MR 1052347 | Zbl 0714.46009

25. A. Seeger, Limiting behaviour of the approximate second-order subdifferential of a convex function, J. Optim. Th. Appl., 1992, 74, pp. 527-544. | MR 1181850 | Zbl 0792.49015

26. M. Sion, On general minimax theorems, Pacifics J. Math., 1958, 8, pp. 171-176. | MR 97026 | Zbl 0081.11502

27. M. Valadier, Sous-différentiels d'une borne supérieure et d'une somme continue de fonctions convexes, C. R. Acad. Sci. Paris, Série A, 1969, 268, pp. 39-42. | MR 241975 | Zbl 0164.43302

28. M. Volle, Convergence en niveaux et en épigraphes, C R. Acad. Sci.Paris, Série I, 1984, 299, pp. 295-298. | MR 761250 | Zbl 0566.49004

29. M. Volle, Quelques résultats relatifs à l'approche par les tranches de l'épi-convergence, Contributions à la dualité en optimisation et à l'épi-convergence, Thèse d'état, Université de Pau, 1986.

30. M. Volle, Approximations quasi-infconvolutives, Publication du Département de Mathématiques de l'Université de Limoges, 1986.

31. C. Zalinescu, Programare metematiča în spatii normate infinit dimensionale (In Roumain), manuscript in preparation.

32. J. Zowe, Nondifferentiable optimization - A motivation and a short introduction into the subgradient and the bundie concept, Computational Mathematical Programming, K. SCHITTKOWSKI, Ed., Springer-Verlag, Berlin, 1985. | MR 820049 | Zbl 0581.90072