Computer Sciences Dept.

Unconstrained Lagrangians in Nonlinear Programming

Olvi Mangasarian

The main purpose of this work is to associate a wide class of Lagrangian functions with a nonconvex, inequality and equality constrained optimization problem in such a way that unconstrained stationary points of each Lagrangian are related to Kuhn-Tucker points or local or global solutions of the optimization problem. As a consequence of this we are able to obtain duality results and two computational algorithms for solving the optimization problem. One algorithm is a Newton algorithm which has a local superlinear or quadratic rate of convergence. The other method is a locally linearly convergent method for finding stationary points of the Lagrangian and is an extension of the method of multipliers of Hestenes and Powell to inequalities.

Download this report (PDF)

Return to tech report index

Computer Science | UW Home