Condizioni di convessità nella programmazione dinamica

Giovanni Marro; Remo Rossi

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti (1973)

  • Volume: 54, Issue: 4, page 604-614
  • ISSN: 0392-7881

Abstract

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The convexity of return functions in dynamic programming implies the possibility of employing standard procedures of convex programming for the searches of minima of functions which are performed at every stage of the computational procedure. In the present work by means of a geometric approach are derived necessary and sufficient conditions for the convexity of return functions in dynamic optimization problems with bounded states and controls and in presence of isoperimetric constraints.

How to cite

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Marro, Giovanni, and Rossi, Remo. "Condizioni di convessità nella programmazione dinamica." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti 54.4 (1973): 604-614. <http://eudml.org/doc/293812>.

@article{Marro1973,
author = {Marro, Giovanni, Rossi, Remo},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti},
language = {ita},
month = {4},
number = {4},
pages = {604-614},
publisher = {Accademia Nazionale dei Lincei},
title = {Condizioni di convessità nella programmazione dinamica},
url = {http://eudml.org/doc/293812},
volume = {54},
year = {1973},
}

TY - JOUR
AU - Marro, Giovanni
AU - Rossi, Remo
TI - Condizioni di convessità nella programmazione dinamica
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti
DA - 1973/4//
PB - Accademia Nazionale dei Lincei
VL - 54
IS - 4
SP - 604
EP - 614
LA - ita
UR - http://eudml.org/doc/293812
ER -

References

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  1. KUHN, H. W. e TUCKER, A. W., Nonlinear programming, «Proceedings of the 2-nd Berkeley Symposium on Mathematical Statistics and Probability», University of California Press,, Berkeley, 481-492 (1951). MR47303
  2. WOLFE, P., Computational techniques for nonlinear programs, «Princeton University Conference on Linear Programming» (1957). 
  3. WOLFE, P., Recent development in non-linear programming, The RAND Corporation Santa Monica, P-2063 (1960). 
  4. ROSEN, J. B., Optimal control and convex programming, «Proceedings of the IBM Scientific Computing Symposium on Control Theory and Applications», Yorktown Heights, N.Y., 223-237 (1964). MR218135
  5. DANTZIG, G. B., Linear control processes and mathematical programming, «Journal SIAM on Control», 4 (1) (1966). MR189858
  6. TORNG, H. C., Optimization of discrete control systems through linear programming, «Journal of the Franklin Institute», 278 (1), 28-44 (1964). 
  7. LEE, E. B., A sufficient condition in the theory of optimal control, «Journal SIAM on Control», I (3), 241-245 (1963). Zbl0151.13105MR175693
  8. LEE, E. B., Linear optimal control problems with isoperimetric constraints, «IEEE Transactions», AC-12 (1), 87-90 (1967). MR209036DOI10.1109/tac.1967.1098488
  9. HO, Y. C., A successive approximation technique for optimal control systems subject to input saturation, «Transactions of the ASME, Journal of Basic Engineering», 84 (1), 33-40 (1962). MR136021
  10. ROSEN, J. B., Iterative solution of nonlinear optimal control problems, «Journal SIAM on Control», 4 (1), 223-244 (1966). Zbl0229.49025MR189877
  11. GILBERT, E. G., An iterative procedure for computing the minimum of a quadratic form on a convex set, «Journal SIAM on Control», 4 (1), 61-80 (1966). Zbl0196.51204MR189875
  12. BARR, R. O., Computation of optimal controls on convex reachable sets, «Mathematical Theory of Control», Academic Press, New York, 63-70 (1967). MR252071
  13. BARR, R. O. e GILBERT, E. G., Some iterative procedures for computing optimal controls, «Proceedings of the 3-rd IFAC Symposium», London1966. MR378410
  14. BARR, R. O. e GILBERT, E. G., Some efficient algorithms for a class of abstract optimization problems arising in optimal control, «IEEE Transactions», AC-14 (6), 640-652 (1969). MR349011DOI10.1109/tac.1969.1099299
  15. MARRO, G. e ROSSI, R., Sulla ottimizzazione dei sistemi discreti. Parte I: Sistemi lineari con vincoli convessi, «Calcolo», 4 (3) (1967). Zbl0164.39804MR292562DOI10.1007/BF02576035
  16. MARRO, G. e ROSSI, R., Sulla ottimizzazione dei sistemi discreti. Parte II: Sistemi non lineari, «Calcolo», 4 (4) (1967). MR297438DOI10.1007/BF02575665
  17. BERNHOLTZ, B. e GRAHAM, L. J., Hydrothermal economic scheduling. Part I: Solution by incremental dynamic programming, «AIEE Transactions», part. III, 79, 921-931 (1960). 
  18. BERNHOLTZ, B. e GRAHAM, L. J., Hydrothermal economic scheduling. Part II: Extension of the basic theory, «AIEE Transactions», part III, 80, 1089-1096 (1962). 
  19. BERNHOLTZ, B. e GRAHAM, L. J., Hydrothermal economic scheduling. Part III: Scheduling the thermal subsystem using constrained steepest descent, «AIEE Transactions », part III, 80, 1096-1105 (1962). 
  20. BERNHOLTZ, B. e GRAHAM, L. J., Hydrothermal economic scheduling. Part IV: A continuous procedure for maximizing the weighted output of a hydrolectric generating station, «AIEE Transactions», part III, 80, 1105-1107 (1962). 

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