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 and local saddlepoints 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.

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