SECOND-ORDER CONDITIONS FOR CONSTRAINED MINIMA.
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)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jun 01, 1967
- Accession Number
- AD0658069
Entities
People
- Garth P. Mccormick