LAGRANGE MULTIPLIERS AND NONCONVEX PROGRAMS.
RESEARCH ANALYSIS CORP MCLEAN VA
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The paper contains two new theoretical results that have implications in nonlinear programming. The first result stems from a generalization of the notion of conjugacy and yields the fact that the second conjugate of a nonconvex function is essentially identical to the convex envelope of that function. This is used to obtain the second result, which illustrates the reasons for the failure of the Lagrange multiplier technique on certain nonconvex programs. It is shown that the application of this technique optimizes the convex envelope of the objective function rather than the objective function itself. Author
- Operations Research