Rockafellar, R. Tyrrell(1-WA-AM)
Lagrange multipliers and optimality. (English summary)
SIAM Rev. 35 (1993), no. 2, 183--238.
49-02 (49N15 90C30)
The author presents a very interesting review on the role of Lagrange multipliers in optimization. He tries to show how their role has come to be understood from many different angles. The emphasis lies not only on the properties of Lagrange multipliers that can be drawn upon in applications and numerical work, but also on the new kind of analysis that has had to be developed. The framework consists of optimization problems in finite dimensions. The author treats the classical theory, multiplier rules with normal cones, applications to game theory, the significance of Lagrange multipliers for the parametric study of problems of optimization, augmented Lagrangians, and multipliers as subgradients. This paper is an expanded version of the author's John von Neumann Lecture (presented at the 1992 Annual Meeting of SIAM, Los Angeles, CA, 1992).