Extension of quasi-Newton methods to constrained optimization and to general systems of nonlinear equations and inequalities. Final report, February 1, 1976--January 31, 1977
A theory for extending the popular quasi-Newton secant methods, including the Davidon--Fletcher--Powell method and the Broyden--Fletcher--Goldfarb--Shanno method, for unconstrained minimization to constrained minimization was developed. Since these standard methods must work with positive definite matrices and the usual formulation of the first-order conditions for constrained optimization problems does not lead to a positive definite matrix, a very important part of the theory was the exploitation of positive definite subproblems. The theory is modular, and as a consequence one can now extend an algorithm for unconstrained optimization to constrained optimization in an effective manner.
- Research Organization:
- Rice Univ., Houston, Tex. (USA). Dept. of Mathematical Sciences
- OSTI ID:
- 5345258
- Report Number(s):
- ORO-5046-4
- Country of Publication:
- United States
- Language:
- English
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