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Generalized geometric programming applied to problems of optimal control. I: Theory. (English) Zbl 0369.90120

MSC:
90C30Nonlinear programming
49-00Reference works (calculus of variations)
49JxxExistence theory for optimal solutions
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References:
[1] Fenchel, W.,Convex Cones, Sets, and Functions, Princeton University, Princeton, New Jersey, Mathematics Department, Mimeographed Lecture Notes, 1951. · Zbl 0053.12203
[2] Rockafellar, R. T.,Convex Analysis, Princeton University Press, Princeton, New Jersey, 1970. · Zbl 0193.18401
[3] Peterson, E. L.,Geometric Programming, SIAM Review, Vol. 18, pp. 1-51, 1976. · Zbl 0331.90057 · doi:10.1137/1018001
[4] Rockafellar, R. T.,Conjugate Convex Functions in Optimal Control and the Calculus of Variations, Journal of Mathematical Analysis and Applications, Vol. 32, pp. 174-222, 1970. · Zbl 0218.49004 · doi:10.1016/0022-247X(70)90324-0
[5] Vinter, R. B.,Application of Duality Theory to a Class of Composite Cost Control Problems, Journal of Optimization Theory and Applications, Vol. 13, pp. 436-460, 1974. · Zbl 0259.49022 · doi:10.1007/BF00934940
[6] Van Slyke, R. M., andWets, R. J. B.,A Duality Theory for Abstract Mathematical Programs with Applications to Optimal Control Theory, Journal of Mathematical Analysis and Applications, Vol. 22, pp. 679-706, 1968. · Zbl 0157.16004 · doi:10.1016/0022-247X(68)90206-0
[7] Mossino, J.,An Application of Duality to Distributed Optimal Control Problems with Constraints on the Control and the State, Journal of Mathematical Analysis and Applications, Vol. 50, pp. 223-242, 1975. · Zbl 0304.49003 · doi:10.1016/0022-247X(75)90019-0
[8] Jefferson, T. R., andScott, C. H.,Generalized Geometric Programming Applied to Problems of Optimal Control, II, Computational Aspects (to appear).
[9] Rockafellar, R. T.,Integrals Which Are Convex Functionals, Pacific Journal of Mathematics, Vol. 24, pp. 525-539, 1968. · Zbl 0159.43804
[10] Rockafellar, R. T.,Convex Functionals and Duality, Contributions to Nonlinear Functional Analysis, pp. 215-236, Academic Press, New York, New York, 1971.