Accession Number : AD0678570

Title :   LAGRANGE MULTIPLIERS AND NONCONVEX PROGRAMS.

Descriptive Note : Technical paper,

Corporate Author : RESEARCH ANALYSIS CORP MCLEAN VA

Personal Author(s) : Falk,James E.

Report Date : NOV 1968

Pagination or Media Count : 26

Abstract : 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)

Descriptors :   (*NONLINEAR PROGRAMMING, THEOREMS), CONVEX SETS, PARTIAL DIFFERENTIAL EQUATIONS, NUMERICAL ANALYSIS, ALGORITHMS

Subject Categories : Operations Research

Distribution Statement : APPROVED FOR PUBLIC RELEASE