×

Idempotent analysis as a tool of control theory and optimal synthesis. II. (English. Russian original) Zbl 0709.49015

Funct. Anal. Appl. 23, No. 4, 300-307 (1989); translation from Funkts. Anal. Prilozh. 23, No. 4, 53-62 (1989).
[For part I see Funkts. Anal. Prilozh. 23, No.1, 1-14 (1989; Zbl 0692.49022).]
The Cauchy problem is considered for the Bellman’s homogeneous differential equation using a new superposition principle for solutions. Its application to discrete optimization problems with large parameter is demonstrated.
Reviewer: S.Patarinski

MSC:

49L20 Dynamic programming in optimal control and differential games
49J15 Existence theories for optimal control problems involving ordinary differential equations
49K05 Optimality conditions for free problems in one independent variable
90C09 Boolean programming

Citations:

Zbl 0692.49022
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] V. N. Kolokol’tsov and V. P. Maslov, ”Idempotent analysis as a tool of control theory. 1,” Funkts. Anal. Prilozhen.,22, No. 4, 1-14 (1988). · Zbl 0667.58018 · doi:10.1007/BF01077717
[2] S. M. Avdoshin, V. V. Belov, and V. P. Maslov, Mathematical Aspects of Synthesis of Computing Media [in Russian], Izd. MIEM, Moscow (1984). · Zbl 0597.49001
[3] V. P. Maslov, Asymptotic Methods for Solution of Pseudodifferential Equations [in Russian], Nauka, Moscow (1987). · Zbl 0625.35001
[4] V. P. Maslov, ”On a new superposition principle for optimization problems,” Usp. Mat. Nauk,42, No. 3, 39-48 (1987). · Zbl 0707.35138
[5] S. M. Avdoshin, V. V. Belov, V. P. Maslov, and V. M. Piterkin, Optimization of Flexible Production Systems [in Russian], Izd. MIEM, Moscow (1987).
[6] M. Gardner, Mathematical Pastimes [Russian translation], Moscow (1972).
[7] V. N. Kolokol’tsov and V. P. Maslov, ”The Cauchy problem for the homogeneous Bellman equation,” Dokl. Akad. Nauk SSSR,296, No. 4, 796-800 (1987).
[8] I. Ekeland and R. Temam, Analyse convexe et problemes variationels, Dunod, Paris (1974). · Zbl 0281.49001
[9] A. S. Filippov, Diferential Equations with Discontinuous Right-Hand Side [in Russian], Nauka, Moscow (1983).
[10] M. G. Crandall and P. L. Lions, ”Viscosity solutions of Hamilton-Jacobi equations,” Trans. Am. Math. Soc.,27, 1-40 (1983). · Zbl 0599.35024 · doi:10.1090/S0002-9947-1983-0690039-8
[11] L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze, and E. F. Mishchenko, The Mathematical Theory of Optimal Processes [in Russian], Nauka, Moscow (1969).
[12] V. V. Voevodin, Parallel Structures of Algorithms and Programs [in Russian], Izd. OVM Akad. Nauk SSSR (1987). · Zbl 0705.68055
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.