Extremal problems with D.C.-constraints

Computational Mathematics and Mathematical Physics

Volumn 41, Issue 12, 2001, Pages 1742-1751

  Strekalovsky, A S ^a  

^a MATROSOV INSTITUTE FOR SYSTEM DYNAMICS AND CONTROL THEORY   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33746531827     PISSN: 09655425     EISSN: 15556662     Source Type: Journal    
DOI: None     Document Type: Article

References (21)

1. Rockafellar, R.T., Convex Analysis, Princeton: Princeton Univ. Press, 1970. Translated under the title Vypuklyi analiz, Moscow: Mir, 1973.
2. Alekseev, V.M., Tikhomirov, V.M., and Fomin, S.V., Optimal'noe upravlenie (Optimal Control), Moscow: Nauka, 1979.
3. Clarke, F., Optimization and Nonsmooth Analysis, New York: Wiley, 1983. Translated under the title Optimizatsiya i negladkii analiz, Moscow: Mir, 1983.
4. Pshenichnyi, B.N., Neobkhodimye usloviya ekstremuma (Necessary Extremum Conditions), Moscow: Nauka, 1982.
5. Vasil'ev, F.P., Chislennye melody resheniya extremal'nykh zadach (Numerical Methods for Solving Extremum Value Problems), Moscow: Nauka, 1988.
6. Aleksandrov, A.D., Surfaces Representable as a Difference of Convex Functions, Dokl. Akad. Nauk SSSR, 1950, vol. 72, pp. 613-616.
7. Horst, R. and Tuy, H., Global Optimization (Deterministic Approaches), Berlin: Springer, 1993, 2nd ed.
8. Horst, R., Pardalos, P., and Thoai, N., Introduction to Global Optimization, Dordrecht: Kluwer, 1995.
9. Handbook of Global Optimization, Horst, R. and Pardalos, P., Eds., Dordrecht: Kluwer, 1995.
10. Hiriart-Urruty, J.-B., Generalized Differentiability. Duality and Optimization for Problems Dealing with Difference of Convex Functions, Lect. Notes in Economics and Math. Systems, Berlin: Springer, 1985, vol. 256, pp. 37-69.
11. Hiriart-Urruty, J.-B. and Lemarechal, C., Convex Analysis and Minimization Algorithms, Berlin: Springer, 1993.
12. Hiriart-Urruty, J.-B., Conditions for Global Optimality 2, Workshop on Global Optimization, Trier (Germany), Toulouse Univ., 1997.
13. Dur, M., Horst, R., and Locaftelli, M., Necessary and Sufficient Global Optimality Conditions for Convex Maximization Revisited, J. Math. Anal. Appl., 1998, vol. 217, pp. 637-649.
14. Merenkov, A.P. and Khamiev, V.Ya., Teoriya gidravlicheskikh tsepei (Theory of Hydraulic Circuits), Moscow: Nauka, 1975.
15. Strekalovsky, A.S., On Global Extremum Value Problem, Dokl. Akad. Nauk SSSR, 1987, vol. 929, no. 5, pp. 1062-1066.
16. Strekalovsky, A.S., On Global Optimization in Nonconvex Problems, Izv. Vyssh. Uchebn. Zaved., Mat., 1990, no. 8, pp. 74-80.
17. Strekalovsky, A.S., On Extremum Value Problems on Complements of Convex Sets, Kibernetika i Sistemnyi Analiz, 1993, no. 1, pp. 113-126.
18. Strekalovsky, A.S., Global Optimality Conditions in d.c.-Programming Problems, Optimizatsiya i upravlenie (Optimization and Control), Irkutsk: Irkutskii Gos. Univ., 1997, issue 1.
19. Hiriart-Urruty, J.-B. and Ledyaev, Y.A., Note on the Characterization of the Global Maxima of a (Tangentially) Convex Function over a Convex Set, J. Convex Anal., 1996, vol. 3, no. 1, pp. 55-61.
20. Tsevendorj, I., On the Global Optimality Conditions, J. Mongolian Math. Soc., 1998, no. 2, pp. 58-62.
21. Strekalovsky, A., Global Optimality Conditions for Nonconvex Optimization, J. Global Optimizat., 1998, no. 12, pp. 415-434.