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An application of conjugate duality for numerical solution of continuous convex optimal control problems. (English) Zbl 0464.49027

49M29 Numerical methods involving duality
90C55 Methods of successive quadratic programming type
49K15 Optimality conditions for problems involving ordinary differential equations
90C25 Convex programming
49J45 Methods involving semicontinuity and convergence; relaxation
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[1] E. Asplund R. T. Rockafellar: Gradients of convex functions. Trans. Amer. Math. Society 189, (1969), 443-467. · Zbl 0181.41901
[2] I. Ekeland R. Temam: Analyse Convexe et Problèmes Variationnels. Dunod, Paris 1974. · Zbl 0281.49001
[3] N. Eldin: A report on the convex feedback method with applications. Proc. 2nd IFAC/IFIP Symposium Optimization Methods (Applied Aspscts), Pergamon Press, Oxford 1979.
[4] T. Glad: Constrained Optimization Using Multiplier Methode with Applications to Control Problems. Lunds Tekniska Högskola Press, Lund 1976.
[5] W. Heins S. K. Mitter: Conjugate convex functions, duality and optimal control problems I. Information Sciences 2 (1970), 211-243. · Zbl 0218.49005
[6] C. Lemarechal: An Algorithm for minimizing convex functions. Information Processing 74, Proc. of ths IFIP Congress 1974. North Holland, Amsterdam. · Zbl 0297.65041
[7] C. Lemarechal: Nondifferentiable optimization, subgradient and \(\epsilon\)-subgradient methods. Lecture Notes: Numerical Methods in Optimization and Opsrations Research. Springer-Verlag, Berlin 1975.
[8] D. E. Luenbsrger: Optimization by Vector Space Methods. J. Wiley and Sons, N. Y. 1968.
[9] J. J. Moreau: Proximité et dualité dans un espace Hilbertien. Bull. Soc. Math. France 93 (1965), 273-299. · Zbl 0136.12101
[10] J. V. Outrata: A multiplier method for convex optimal control problems. Proc. 2nd IFAC/IFIP Symposium Optimization Methods (Applied Aspects), Pergamon Press, Oxford 1979.
[11] J. V. Outrata: On the differentiability in dual optimal control problems. Math. Operationsforsch. Statist., Ser. Optimization 10 (1979), 527-540. · Zbl 0435.49036
[12] R. T. Rockafellar: Integrals which are convex functionals. Pac. J. of Math. 24 (1968), 525-539. · Zbl 0159.43804
[13] R. T. Rockafellar: Conjugate convex functions in optimal control and the calculus of variations. J. of Math. Anal, and Appl. 32 (1970), 174-222. · Zbl 0218.49004
[14] R. T. Rockafellar: A dual approach to solving nonlinear programming problems by unconstrained optimization. Math. Programming 5 (1973), 354-373. · Zbl 0279.90035
[15] R. T. Rockafellar: The multiplier method of Hestens and Powell applied to convex programming. J. Optimiz. Theory and Appl. 12 (1973), 555-562. · Zbl 0254.90045
[16] R. T. Rockafellar: Conjugate Duality and Optimization. SIAM/CBMS monograph series No 16, SIAM Publications, 1974. · Zbl 0296.90036
[17] R. D. Rupp: A method for solving a quadratic optimal control problem. J. Optimiz. Theory and Appl. 9 (1972), 251-264. · Zbl 0217.46802
[18] R. D. Rupp: A nonlinear optimal control minimization technique. Trans. AMS 775 (1973), 357-381. · Zbl 0273.49049
[19] T. Tanino H. Nakayama Y. Sawaragi: Multiplier functions and duality for non-linear programmes having a set constraint. Ing. J. Syst. Sci. 9 (1978), 467-481. · Zbl 0374.90059
[20] A. P. Wierzbicki S. Kurcyusz: Projection on a cone, penalty functionals and duality theory for problems with inequality constraints in Hilbert space. SIAM J. Contr. and Optimiz. 75 (1977), 25-56. · Zbl 0355.90045
[21] P. Wolfe: A method of conjugate subgradients for minimizing nondifferentiable functions. Math. Programming Study 3 (1975), 145-173. · Zbl 0369.90093
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