SECOND-ORDER CONDITIONS FOR CONSTRAINED MINIMA.
RESEARCH ANALYSIS CORP MCLEAN VA
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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 fchi subject to the constraints g sub ichi or 0, i 1,...,m, and h sub jchi 0, j1,...,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
- Theoretical Mathematics
- Operations Research