| Title:
|
An application of conjugate duality for numerical solution of continuous convex optimal control problems (English) |
| Author:
|
Outrata, Jiří V. |
| Author:
|
Kříž, Otakar F. |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
16 |
| Issue:
|
6 |
| Year:
|
1980 |
| Pages:
|
(477)-497 |
| . |
| Category:
|
math |
| . |
| MSC:
|
49D30 |
| MSC:
|
49J45 |
| MSC:
|
49K15 |
| MSC:
|
49M29 |
| MSC:
|
90C25 |
| MSC:
|
90C55 |
| idZBL:
|
Zbl 0464.49027 |
| idMR:
|
MR607289 |
| . |
| Date available:
|
2009-09-24T17:17:14Z |
| Last updated:
|
2012-06-05 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/125303 |
| . |
| Reference:
|
[1] E. Asplund R. T. Rockafellar: Gradients of convex functions.Trans. Amer. Math. Society 189, (1969), 443-467. MR 0240621 |
| Reference:
|
[2] I. Ekeland R. Temam: Analyse Convexe et Problèmes Variationnels.Dunod, Paris 1974. MR 0463993 |
| Reference:
|
[3] N. Eldin: A report on the convex feedback method with applications.Proc. 2nd IFAC/IFIP Symposium Optimization Methods (Applied Aspscts), Pergamon Press, Oxford 1979. |
| Reference:
|
[4] T. Glad: Constrained Optimization Using Multiplier Methode with Applications to Control Problems.Lunds Tekniska Högskola Press, Lund 1976. |
| Reference:
|
[5] W. Heins S. K. Mitter: Conjugate convex functions, duality and optimal control problems I.Information Sciences 2 (1970), 211-243. MR 0271808 |
| Reference:
|
[6] C. Lemarechal: An Algorithm for minimizing convex functions.Information Processing 74, Proc. of ths IFIP Congress 1974. North Holland, Amsterdam. Zbl 0297.65041, MR 0441343 |
| Reference:
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[7] C. Lemarechal: Nondifferentiable optimization, subgradient and $\epsilon$-subgradient methods.Lecture Notes: Numerical Methods in Optimization and Opsrations Research. Springer-Verlag, Berlin 1975. MR 0496691 |
| Reference:
|
[8] D. E. Luenbsrger: Optimization by Vector Space Methods.J. Wiley and Sons, N. Y. 1968. |
| Reference:
|
[9] J. J. Moreau: Proximité et dualité dans un espace Hilbertien.Bull. Soc. Math. France 93 (1965), 273-299. Zbl 0136.12101, MR 0201952 |
| Reference:
|
[10] J. V. Outrata: A multiplier method for convex optimal control problems.Proc. 2nd IFAC/IFIP Symposium Optimization Methods (Applied Aspects), Pergamon Press, Oxford 1979. |
| Reference:
|
[11] J. V. Outrata: On the differentiability in dual optimal control problems.Math. Operationsforsch. Statist., Ser. Optimization 10 (1979), 527-540. Zbl 0435.49036, MR 0568630 |
| Reference:
|
[12] R. T. Rockafellar: Integrals which are convex functionals.Pac. J. of Math. 24 (1968), 525-539. Zbl 0159.43804, MR 0236689 |
| Reference:
|
[13] R. T. Rockafellar: Conjugate convex functions in optimal control and the calculus of variations.J. of Math. Anal, and Appl. 32 (1970), 174-222. Zbl 0218.49004, MR 0266020 |
| Reference:
|
[14] R. T. Rockafellar: A dual approach to solving nonlinear programming problems by unconstrained optimization.Math. Programming 5 (1973), 354-373. Zbl 0279.90035, MR 0371416 |
| Reference:
|
[15] R. T. Rockafellar: The multiplier method of Hestens and Powell applied to convex programming.J. Optimiz. Theory and Appl. 12 (1973), 555-562. MR 0334953 |
| Reference:
|
[16] R. T. Rockafellar: Conjugate Duality and Optimization.SIAM/CBMS monograph series No 16, SIAM Publications, 1974. Zbl 0296.90036, MR 0373611 |
| Reference:
|
[17] R. D. Rupp: A method for solving a quadratic optimal control problem.J. Optimiz. Theory and Appl. 9 (1972), 251-264. MR 0301597 |
| Reference:
|
[18] R. D. Rupp: A nonlinear optimal control minimization technique.Trans. AMS 775 (1973), 357-381. Zbl 0273.49049, MR 0322645 |
| Reference:
|
[19] T. Tanino H. Nakayama Y. Sawaragi: Multiplier functions and duality for non-linear programmes having a set constraint.Ing. J. Syst. Sci. 9 (1978), 467-481. MR 0496703 |
| Reference:
|
[20] A. P. Wierzbicki S. Kurcyusz: Projection on a cone, penalty functionals and duality theory for problems with inequality constraints in Hilbert space.SIAM J. Contr. and Optimiz. 75 (1977), 25-56. MR 0438720 |
| Reference:
|
[21] P. Wolfe: A method of conjugate subgradients for minimizing nondifferentiable functions.Math. Programming Study 3 (1975), 145-173. Zbl 0369.90093, MR 0448896 |
| . |
