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2001 | 11 | 4 | 773-801
Tytuł artykułu

Optimization problems with convex epigraphs. Application to optimal control

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
For a class of infinite-dimensional minimization problems with nonlinear equality constraints, an iterative algorithm for finding global solutions is suggested. A key assumption is the convexity of the ''epigraph'', a set in the product of the image spaces of the constraint and objective functions. A convexification method involving randomization is used. The algorithm is based on the extremal shift control principle due to N.N. Krasovskii. An application to a problem of optimal control for a bilinear control system is described.
Rocznik
Tom
11
Numer
4
Strony
773-801
Opis fizyczny
Daty
wydano
2001
otrzymano
2001-06-01
poprawiono
2001-09-01
Twórcy
  • V.A. Steklov Institute of Mathematics, Russian Academy of Sciences, Gubkin Str. 8, 117966 Moscow, Russia
Bibliografia
  • Bertsekas D.P. (1982): Constrained Optimization and Lagrange Multiplier Methods. — New York: Academic Press.
  • Ermoliev Yu.M., Kryazhimskii A.V. and Ruszczyński A. (1997): Constraint aggregation principle in convex optimization. — Math. Programming, Series B, Vol.76, No.3, pp.353–372.
  • Fedorenko R.P. (1978): Approximate Solution of Optimal Control Problems. — Moscow: Nauka, (in Russian).
  • Gabasov R., Kirillova F.M. and Tyatyushkin A.I. (1984): Constructive Optimization Problems, Part 1: Linear Problems. — Minsk: Universitetskoye, (in Russian).
  • Krasovskii N.N. (1985): Control of Dynamical Systems. — Moscow: Nauka, (in Russian).
  • Krasovskii N.N. and Subbotin A.I. (1988): Game-Theoretical Control Problems. — Berlin: Springer.
  • Kryazhimskii A.V. (1999): Convex optimization via feedbacks. — SIAM J. Contr. Optim., Vol.37, No.1, pp.278–302.
  • Kryazhimskii A.V. and Maksimov V.I. (1998): An iterative procedure for solving control problem with phase constraints. — Comp. Math. Math. Phys., Vol.38, No.9, pp.1423– 1428.
  • Matveyev A.S. and Yakubovich V.A. (1998): Nonconvex problems of global optimization in control theory. — Modern Mathematics and Its Applications, All-Russian Institute for Scientific and Technical Information, Vol.60, pp.128–175, (in Russian).
  • Pontryagin L.S., Boltyanskii V.G., Gamkrelidze R.V. and Mishchenko E.F. (1969): Mathematical Theory of Control Processes. — Moscow: Nauka, (in Russian).
  • Sonnevend G. (1986): An “analytic center” for polyhedrons and new classes of global algorithms for linear (smooth convex) programming. — Proc. 12th Conf. System Modelling and Optimization, Budapest, 1985, Berlin: Springer, LNCIS, Vol.84, pp.866–876.
  • Vasiliev F.P. (1981): Solution Methods for Extremal Problems. — Moscow, Nauka, (in Russian).
  • Warga J. (1975): Optimal Control of Differential and Functional Equations. — New York: Academic Press.
  • Zangwill W.I. and Garcia C.B. (1981): Pathways to Solutions, Fixed Points and Equilibria. — Englewood Cliffs: Prentice-Hall.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-amcv11i4p773bwm
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