THEORY OF LAGRANGE MULTIPLIERS FOR CONSTRAINED OPTIMIZATION PROBLEMS
RESEARCH ANALYSIS CORP MCLEAN VA
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The paper treats an extension of one version of the classical Lagrange multiplier rule as applied to nonlinear programming problems. For a given problem, an auxiliary problem is defined and its properties are studied under various assumptions. In particular, when the given problem has a strictly convex objective function and concave constraints it is shown that the auxiliary problem is one of maximizing a concave differentiable function over an open set subject only to nonnegativity conditions. Some applications of this theory are presented only with the connection between the auxiliary problem and a dual of the given problem.
- Theoretical Mathematics
- Operations Research