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

Technical Report ·

OSTI ID:5345258

Tapia, R A

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
• DOE Contract Number: EY-76-S-05-5046
• OSTI ID: 5345258
• Report Number(s): ORO-5046-4
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE
NEWTON METHOD
OPTIMIZATION
NONLINEAR PROBLEMS
ALGORITHMS
MATRICES
ITERATIVE METHODS
MATHEMATICAL LOGIC
990200* - Mathematics & Computers