SECOND ORDER SUFFICIENT CONDITIONS FOR WEAK AND STRICT CONSTRAINED MINIMA.
Systems research memo.,
NORTHWESTERN UNIV EVANSTON ILL TECHNOLOGICAL INST
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Recently, for x epsilon E to the the nth power, McCormick proved a theorem giving sufficient secord order i.e., depending on twice differentiability conditions for a strict local minimum of a function constrained by equality and inequality constraints. A different development and proof can be found in the book by Hestenes. In Theorem 1 following, second order conditions are given for a weak local constrained minimum. The proof closely parallels the proof given by McCormick in, the essential modification of the conditions and proof involving regulatory assumptions on the behavior of the Hessian of the associated Lagrangian function of the problem, in a suitable feasible neighborhood of the minimizing point. The proof of this result, slightly modified, leads to Theorem 2 which provides a neighborhood characterization for a strict local constrained minimum. Several corollaries follow, Corollary 1 being the above-indicated theorem proved by McCormick and Hestenes. Author
- Numerical Mathematics