Global optimization of functions with concave support minorant

O. V. Khamisov

Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 44 (2004) no. 9, pp. 1552-1563

Bibliographie

[1] Bulatov V. P., “Metody resheniya mnogoekstremalnykh zadach (globalnyi poisk)”, Metody optimizatsii i ikh prilozheniya, v. 1, Matematicheskoe programmirovanie, Nauka, Novosibirsk, 1989, 131–157

[2] Mikhalevich V. S., Gupal A. M., Norkin V. I., Metody nevypukloi optimizatsii, Nauka, M., 1987 | MR | Zbl

[3] Piyavskii S. A., “Odin algoritm otyskaniya ekstremuma funktsii”, Zh. vychisl. matem. i matem. fiz., 12:4 (1972), 888–896

[4] Strongin R., Chislennye metody v mnogoekstremalnykh zadachakh, Nauka, M., 1978 | MR | Zbl

[5] Sukharev A., Minimaksnye algoritmy v zadachakh chislennogo analiza, Nauka, M., 1989 | MR | Zbl

[6] Hansen P., Laumard B., “Lipschitz optimization”, Handbook of Global Optimizat., Kluwer Academ. Publs., Dordrecht, 1995, 407–493 | MR | Zbl

[7] Pintér J., Global optimization in action, Kluwer Academ. Publs., Dordrecht, 1995 | MR

[8] Wood G., “Estimation of the Lipschitz constant of a function”, J. Global Optimizat., 22:1 (2002), 271–284 | DOI | Zbl

[9] Tkhach F., Tui X., “Relefnyi indikatornyi metod — novyi podkhod v globalnoi optimizatsii”, Optimizatsiya, modeli, metody, resheniya, Nauka, Novosibirsk, 1992, 221–235 | MR

[10] Goudin E., Jaumard, Ellaia R., “Global optimization of Hölder function”, J. Global Optimizat., 4 (1996), 323–348 | DOI | MR

[11] Aleksandrov P. S., Vvedenie v teoriyu mnozhestv i obschuyu topologiyu, Nauka, M., 1977 | MR

[12] Hirriart-Urruty J.-B., “Generalized differentiability, duality and optimization for problems dealing with difference of convex functions”, Lect. Notes in Economics and Math. Systems, 256, 1985, 37–70 | MR

[13] Horst R., Tuy H., Global optimization (deterministic approaches), Springer, Berlin, 1996 | MR

[14] Tuy H. D. C., “Optimization: theory methods and algorithms”, Handbook of Global Optimizat., Kluwer Academ. Publs., Dordrecht, 1995, 149–216 | MR | Zbl

[15] Lamar B. W., “A method for converting a class of univariate functions into d.c. functions”, J. Global Optimizat., 15 (1999), 55–71 | DOI | MR | Zbl

[16] Baritompa W., Cutler A., “Accelerations for global optimization covering methods using second derivatives”, J. Global Optimizat., 4 (1994), 329–342 | DOI | MR

[17] Gergel V. P., “A global optimization algorithm for multivariate functions with Lipschitzian first derivatives”, J. Global Optimizat., 10 (1997), 257–281 | DOI | MR | Zbl

[18] Beckenbach E. F., “Generalized convex functions”, Bull. Amer. Math. Soc., 43 (1937), 363–371 | DOI | MR

[19] Zabotin Ya., Khababulin P., “Nelineinye opornye funktsionaly i zadachi optimizatsii”, Issl. po prikl. matem., 3, Un-t, Kazan, 1975, 60–67 | MR

[20] Ben-Tal A., Ben-Israel A., “$F$-convex functions: properties and applications”, Generalized Concavity in Optimizat. and Economics, Academ Press, New York, 1981, 301–334

[21] Dolecki S., Kurcyusz S., “On $\Phi$ convexity in extremal problems”, SIAM J. Control and Optimizat., 16:2 (1978), 277–300 | DOI | MR | Zbl

[22] Khamisov O., “O svoistvakh funktsii s vognutoi minorantoi”, Kachestvennye metody issl. sistem differents. ur-nii, Nauka, Novosibirsk, 1994, 71–77

[23] Norkin V., “O metode Piyavskogo dlya resheniya obschikh zadach globalnoi optimizatsii”, Zh. vychisl. matem. i matem. fiz., 32:7 (1992), 992–1006 | MR | Zbl

[24] Ekeland I., Temam R., Convex analysis and variational problems, Elsevier, New York, 1976 | MR | Zbl

[25] Kutateladze S., Rubinov A., Dvoistvennost Minkovskogo i ee prilozheniya, Nauka, Novosibirsk, 1976 | MR

[26] Vial J.-F., “Strong and weak convexity of sets and functions”, Math. Operat. Res., 8:2 (1983), 231–259 | DOI | MR | Zbl

[27] Levitin E. C., Polyak B. T., “Metody minimizatsii pri nalichii ogranichenii”, Zh. vychisl. matem. i matem. fiz., 6:5 (1966), 787–823 | MR | Zbl

[28] Pshenichnyi B. N., Danilin Yu. M., Chislennye metody v ekstremalnykh zadachakh, Nauka, M., 1975 | MR | Zbl

[29] Nurminskii E. A., “Kvazigradientnyi metod resheniya zadachi nelineinogo programmirovaniya”, Kibernetika, 1973, no. 1, 122–125 | MR | Zbl

[30] Bazara M., Shetti K., Nelineinoe programmirovanie. Teoriya i metody, Mir, M., 1982 | MR | Zbl

[31] Tuy H., “Convex programming with an additional reverse convex constraint”, J. Optimizat. and Techn., 52 (1987), 463–485 | DOI | MR

[32] Piyavskii S. A., “Algoritm globalnogo poiska minimuma funktsii”, Teoriya optimalnykh reshenii, 2, In-t kibernetiki, Kiev, 1967, 13–24