Lagrange principle and necessary conditions

• Autorzy: Tikhomirov V.
• Języki publikacji: EN

Abstrakty

EN

Necessary conditions of extremum (from the times of Fermat and Lagrange till our times) for extremal problems where smoothness is interlaced with convexity, and some type of regularity takes place, correspond to a unique general principle, which is due to Lagrange. This report is devoted to the Lagrange principle in the theory of optimization.

Słowa kluczowe

EN

mathematical programming; convex analysis; calculus of variations; optimal control; Lagrange multiplier rule

• Wydawca: Systems Research Institute, Polish Academy of Sciences
• Czasopismo: Control and Cybernetics
• Rocznik: 2009
• Tom: Vol. 38, no 4B
• Strony: 1589--1605
• Opis fizyczny: Bibliogr. 27 poz.

Twórcy

autor

Tikhomirov V.

• Department of Mechanics and Mathematics, Moscow State University, Vorobyevy Gory, Moscow 119899, Russia,

Bibliografia

• ALEKSEEV, V.M., TIKHOMIROV, V.M. and FOMIN, S.V. (1987) Optimal Control. Consultants Bureau.
• ARUTYUNOV, A.I., MAGARIL-ILYAEV, G.G. and TIKHOMIROV, V.M. (2006) Pontryagin maximum principle. Proofs and applications (in Russian). Factorial, Moscow.
• BERNOULLI, J. (1696) Problema novum, ad cuius solutionem Mathematici in-vitatur. Acta Eruditorum. (Opera torn. I).
• BRINKHUIS, J. and TIKHOMIROV, V.M, (2005) Optimization: Insight and Applications. Princeton.
• CAUCHY, A.L. (1823) Resumé des Lecons Données a L’Éole Royale Polytechnique sur le Calcul Infinitésimal. Reprinted in: A.L. Cauchy, Oeuvres, Series 2, 4 (1899).
• DUBOVITSKY, A.YA. and MILUTIN, A.A. (1965) Problems for extremum under constraints (in Russian). Zh. Vichisl. Mat. i Mat. Fiz., 5,3, 395-453.
• EULER, L. (1744) Methodus inveniendi ... Lausanne.
• FERMAT, P. (1891) Oevres de Fermat, 1, Gauthier-Villars, Paris.
• FRECHET, V. (1912) Sur la notion de differentielle. Nouvelle annale de mathematique, Ser. 4, V.XII.1912, p. 845.
• GRAVES, L.M. (1950) Some mapping theorems. Duke Math. J., 17, 111-114.
• IOFFE, A.D. and TIKHOMIROV, V.M. (1979) Theory of Extremal Problems. North-Holland.
• JOHN, F. (1948) Extremum problems with inequalities as subsidary conditions. Studies an Essays. Courant Anniversary volume. Interscience, NY, 187-204.
• KANTOROVICH, L.V.(1939) Mathematical methods of production management and planning (in Russian). Leningrad Univ., Leningrad.
• KARUSH, W.E. (1939) Minima of Functions of Several Variables with Inequalities as Side Conditions. Univ. of Chicago Press.
• KUHN, H.W. and TUCKER, A.W. (1951) Nonlinear Programming. Univ. of California Press, Berkeley, 481-482.
• LAGRANGE, L. (1797) Theorie des fonctions analytiques. Paris.
• LEACH, E. (1961) A note on inverse function theorem. Proc. AMS, 12, 694-697.
• LEIBNIZ, G. (1684) Nova methodus pro maximis et minimis... Acta Eruditorum, 467-473.
• LYAPUNOV, A. A. (1940) On totally additive functions (in Russian). Izv. Akad. Nauk SSSR, Ser. Mat., 4, 465-478.
• LYUSTERNIK, L.A. (1934) Sur les extrémés relatifs des fonctionalles (in Russian). Matem. Sbornik, 41, 390-400.
• MAGARIL-ILYAEV, G.G. and TIKHOMIROV, V.M. (2003) Convex Analysis: Theory and Applications. AMS, Providence.
• MILYUTIN, A.A., DMITRUK, A.V. and OSMOLOVSKY, N.P. (2004) Pontryagin maximum principle in optimal control (in Russian). MGU.
• NEWTON, I. (1736) The Method of Fluxions and infinite series. London.
• PONTRYAGIN, L.S. (1959) Optimal control process (in Russian). Uspekhi mat. nauk, 14.
• ROBINSON, S.M. (1976a) Regularity and stability for convex multivalued functions. Math. Oper. Res. 1, 130-143.
• ROBINSON, S.M. (1976b) Stability theory for systems of inequalities. Part II: differentiable nonlinear systems. SIAM J. Numer. Anal, 13, 497-513.
• WEIERSTRASS, K. (1930) Mathematische Werke. Mayer & Miiller, Berlin.