论文信息 - On the existence and nonexistence of Lagrange multipliers in Banach spaces

On the existence and nonexistence of Lagrange multipliers in Banach spaces

The paper deals with the existence of Lagrange multipliers for a general nonlinear programming problem. Some regularity conditions are formulated which are, in a sense, the weakest to assure the existence of multipliers. A number of related conditions are discussed. The connection between the choice of suitable function spaces and the existence of multipliers is analyzed.

S. Kurcyusz

[1] B. V. Dean,et al. Studies in Linear and Non-Linear Programming. , 1959 .

[2] M. Day,et al. Normed Linear Spaces , 1960 .

[3] L. A. Li︠u︡sternik,et al. Elements of Functional Analysis , 1962 .

[4] B. V. Dean,et al. Studies in Linear and Non-Linear Programming. , 1959 .

[5] Pravin Varaiya,et al. Nonlinear Programming in Banach Space , 1967 .

[6] O. Mangasarian,et al. The Fritz John Necessary Optimality Conditions in the Presence of Equality and Inequality Constraints , 1967 .

[7] D. Luenberger. Optimization by Vector Space Methods , 1968 .

[8] Klaus Ritter,et al. Optimization theory in linear spaces. I , 1969 .

[9] Yoshiyuki Sakawa,et al. Nonlinear programming in Banach spaces , 1969 .

[10] K. Ritter,et al. Optimization theory in linear spaces , 1970 .

[11] Elijah Polak,et al. Computational methods in optimization , 1971 .

[12] B. Craven. Nonlinear programming in locally convex spaces , 1972 .

[13] The ascorbic acid content of normal buck semen. , 1973, Bulletin de l'Academie polonaise des sciences. Serie des sciences biologiques.

[14] Jamie J. Goode,et al. Necessary optimality criteria in mathematical programming in normed linear spaces , 1973 .

[15] R. Weatherwax. General Lagrange multiplier theorems , 1974 .

[16] A. Olbrot,et al. On the closure in W1q of the attainable subspace of linear time lag systems , 1977 .