Accession Number : AD0658069

Title :   SECOND-ORDER CONDITIONS FOR CONSTRAINED MINIMA.

Descriptive Note : Technical paper,

Corporate Author : RESEARCH ANALYSIS CORP MCLEAN VA

Personal Author(s) : McCormick,Garth P.

Report Date : JUN 1967

Pagination or Media Count : 23

Abstract : This paper establishes two sets of 'second-order' conditions--one that is necessary, and the other that is sufficient that a vector chi* be a local minimum to the constrained optimization problem: minimize f(chi) subject to the constraints g sub i(chi) = or > 0, i = 1,...,m, and h sub j(chi) = 0, j=1,...,p where the problem functions are twice continuously differentiable. The necessary conditions extend the well-known results obtained with Lagrange multipliers that apply to equality-constrained optimization problems, and the Kuhn-Tucker conditions that apply to mixed inequality and equality problems when the problem functions are required only to have continuous first derivatives. The sufficient conditions extend similar conditions that have been developed only for equality-constrained problems. Examples of the applications of these sets of conditions are given. (Author)

Descriptors :   (*MATHEMATICAL PROGRAMMING, OPTIMIZATION), (*NONLINEAR PROGRAMMING, OPTIMIZATION), INEQUALITIES, VECTOR SPACES, OPERATORS(MATHEMATICS), MATRICES(MATHEMATICS), THEOREMS

Subject Categories : Theoretical Mathematics
      Operations Research

Distribution Statement : APPROVED FOR PUBLIC RELEASE