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Vinter, R. B.

Application of duality theory to a class of composite cost control problems. (English) Zbl 0259.49022

J. Optimization Theory Appl. 13, 436-460 (1974).
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Cited in 4 Documents

MSC:

90C55 Methods of successive quadratic programming type
90C30 Nonlinear programming
93C05 Linear systems in control theory
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References:

[1] Vidyasagar, M.,Optimal Control by Direct Inversion of a Positive-Definite Operator in a Hilbert Space, Journal of Optimization Theory and Applications, Vol. 7, No. 3, 1971. · Zbl 0198.20302
[2] Pearson, J. D.,Reciprocity and Duality in Control Programming Problems, Journal of Mathematical Analysis and Applications, Vol. 10, No. 2, 1965. · Zbl 0131.10501
[3] Pearson, J. D.,Duality and a Decomposition Technique, SIAM Journal on Control, Vol. 4, No. 1, 1966. · Zbl 0168.34902
[4] 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, No. 3, 1968. · Zbl 0157.16004
[5] Heins, W., andMitter, S. K.,Conjugate Convex Functions, Duality and Optimal Control Problems, 1: Systems Governed by Ordinary Differential Equations, Information Sciences, Vol. 2, No. 1, 1970.
[6] Neustadt, L. W.,Synthesis of Time-Optimal Control Systems, Journal of Mathematical Analysis and Applications, Vol. 1, No. 2, 1960. · Zbl 0100.09903
[7] Neustadt, L. W.,Minimum Effort Control Systems, SIAM Journal on Control, Vol. 1, No. 1, 1962. · Zbl 0145.34502
[8] Brøndsted, A.,Conjugate Convex Functions in Topological Vector Spaces, Matematiskfysiske Meddelelser Udgivet af det Kongelige Danske Videnskabernes Selskab, Copenhagen, Vol. 34, No. 1, 1964. · Zbl 0119.10004
[9] Rockafellar, R. T.,Level Sets and Continuity of Conjugate Convex Functions, Transactions of the American Mathematical Society, Vol. 123, No. 1, 1966. · Zbl 0145.15802
[10] Rockafellar, R. T.,Extension of Fenchel’s Duality Theory for Convex Functions, Duke Mathematical Journal, Vol. 33, No. 1, 1966. · Zbl 0138.09301
[11] Rockafellar, R. T.,Duality and Stability in Extremum Problems Involving Convex Functions, Pacific Journal of Mathematics, Vol. 21, No. 1, 1967. · Zbl 0154.44902
[12] Edwards, R. E.,Functional Analysis, Holt, Rinehart, and Winston, New York, New York, 1965.
[13] Taylor, A. E.,Introduction to Functional Analysis, John Wiley and Sons, New York, New York, 1958. · Zbl 0081.10202
[14] Dunford, N., andSchwartz, J. T.,Linear Operators, Vol. 1, John Wiley and Sons (Interscience Publishers), New York, New York, 1958.
[15] Luenberger, D. E.,Optimization by Vector Space Methods, John Wiley and Sons, New York, New York, 1968. · Zbl 0184.44502
[16] Neustadt, L. W., andPaiewonsky, B. H.,On Synthesizing Time Optimal Controls, Paper presented at the 2nd IFAC Congress, Basle, Switzerland, 1963.
[17] Bellman, R.,Notes on Control Processes?1; On the Minimum of Maximum Deviation, Quarterly of Applied Mathematics, Vol. 14, No. 4, 1957. · Zbl 0077.13702
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