90C30 | Nonlinear programming |
[1] | D.P. Bertsekas and S.K. Mitter, ”A descent numerial method for optimization problems with nondifferentiable cost functionals”,SIAM Journal on Control 11 (1973). ·Zbl 0243.49012 |
[2] | D.P. Bertsekas and S.K. Mitter, ”Steepest descent for optimization problems with nondifferentiable cost functionals”, in:Proceedings of the 5th annual Princeton conference on information and system sciences, March 1971. |
[3] | D.P. Bertsekas, ”Nondifferentiable optimization via approximation”,Mathematical Programming Study 3 (1975) 1–25. ·Zbl 0383.49025 |
[4] | A. Cauchy, ”Méthode générale pour la résolution des systèmes d’équations simultanées”,Comptes Rendus Hebdomadaires des Séances de la Académie des Sciences, Paris, 25 (1847). |
[5] | E.W. Cheney and A.A. Goldstein, ”Newton’s method for convex programming and Tchebysheff approximation”,Numerische Mathematik I (1959) 253–268. ·Zbl 0113.10703 ·doi:10.1007/BF01386389 |
[6] | E.W. Cheney and A.A. Goldstein, ”Tchebycheff approximation and related extremal problems”,Journal of Mathematics and Mechanics 14 (1965) 87–98. ·Zbl 0158.15102 |
[7] | F.H. Clarke, ”Generalized gradients and applications”,Transactions of the American Mathematical Society 205 (1975) 247–262. ·Zbl 0307.26012 ·doi:10.1090/S0002-9947-1975-0367131-6 |
[8] | R. Courant, ”Variational methods for the solution of problems of equilibrium and vibrations”,Bulletin of the American Mathematical Society 49 (1943) 1–23. ·Zbl 0063.00985 ·doi:10.1090/S0002-9904-1943-07818-4 |
[9] | H.B. Curry, ”The method of steepest descent for non-linear minimization problems”,Quarterly of Applied Mathematics 2 (1944–45). |
[10] | V.G. Demyanov, ”On the solution of certain minimax problems”,Kibernetica 2 (1966). |
[11] | V.G. Demyanov, ”Algorithms for some minimax problems”,Journal of Computer and Systems Sciences 2 (1968) 431–433. ·Zbl 0177.23104 |
[12] | J. Dugundji,Topology (Allyn and Bacon, Boston, 1966) p. 234, Th. 4.5. |
[13] | I.I. Eremin, ”The relaxation method for solving systems of inequalities with convex functions on the left sides”,Soviet Mathematics Doklady 6 (1965) 219–222. ·Zbl 0144.30601 |
[14] | A. Feuer, ”Minimizing well-behaved functions”, in:Proceedings of the 12th annual Allerton conference on circuit and system theory, University of Illinois, October 1974. |
[15] | J.J-B. Fourier, ”Solution d’une question particulière du calcul des inégalites, second extrait”, Histoire de l’Académie des Sciences (1824) p. 48. |
[16] | J. Hadamard, ”Memoire sur le probleme d’analyse relatif a l’equilibre des plaques elastiques encastrees”, Adacemie des Sciences de l’Institut de France Ser. 2 vol. 33 (1907). |
[17] | A. Goldstein, ”Cauchy’s method of minimization”,Numerische Mathematik 4 (1962) 146–150, ·Zbl 0105.10201 ·doi:10.1007/BF01386306 |
[18] | A. Goldstein, ”On steepest descent,SIAM Journal on Control Ser. A, 3 (1) (1965) 147–151. ·Zbl 0221.65094 |
[19] | A.A. Goldstein, ”Optimization with corners”, in:Nonlinear programming 2 (Academic Press, New York, 1975) pp.215–230. ·Zbl 0395.90074 |
[20] | L.V. Kantorovich, ”Functional analysis and applied mathematics”,Uspehi Matematičeskih Nauk 3 (1948). ·Zbl 0034.21203 |
[21] | C. Lemarechal, ”An algorithm for minimizing convex functions”, in:Proceedings, International Federation of Information Processing Congress 74 (North-Holland, Amsterdam, 1974) pp. 552–556. |
[22] | C. Lemarechal, ”Note on an extension of Davidon’s method to non-differentiable functions”,Mathematical Programming Study 3 (1975) 95–109. |
[23] | Kaj Madsen, ”Minimax solution of non-linear equations without calculating derivatives”,Mathematical Programming Study 3 (1975) 110–126. ·Zbl 0364.90085 |
[24] | Robert Mifflen, ”An algorithm for constrained optimization with semismooth function”, International Institute for Applied Systems Analysis, Laxenburg, Austria. |
[25] | J. Ortega and W. Rheinboldt,Iterative solution of nonlinear equations (Academic Press, New York, 1970). ·Zbl 0241.65046 |
[26] | B.T. Polyak, ”Minimization of unsmooth functionals”,USSR Computation Mathematics and Mathematical Physics 9 (3) (1969). ·Zbl 0229.65056 |
[27] | E. V. Raik, ”Fejer methods in Hilbert space”,Izvestija Akademii Nauk SSSR Serija Matematičeskaja 3 (1967) 286–293, Fig. 6. ·Zbl 0168.13202 |
[28] | S. Saks,Theory of the integral (Dover, 1964). ·Zbl 1196.28001 |
[29] | N.Z. Shor, ”Convergence rate of the gradient descent method with dilation of the space”,Cybernetics (1970). ·Zbl 0243.90038 |
[30] | N.Z. Shor, ”Utilization of the method of space dilation in the minimization of convex functions”,Cybernetics (1970) 7–15. |
[31] | P. Wolfe, ”A method of conjugate subgradients for minimizing nondifferentiable functions”,Mathematical Programming Study 3 (1975) 145–173. ·Zbl 0369.90093 |
[32] | P. Wolfe, ”An algorithm for the nearest point in a polytope”, IBM Research Center Rep. RC 4887 (June 1974). |