Extending interior point method to nonlinear programming using trust regions
The primal barrier method of interior points developed for linear programming can be extended to solve general nonlinear optimization problems. Our fundamental concept is to recast the idea of affine scaling and view it as the result of using an ellipsoidally shaped trust region on iterative subproblems. The standard logarithmic barrier term added to the objective is retained in our nonlinear formulation to promote centering with respect to bound constraints. Our nonlinear algorithm iteratively solves quadratic subproblems subject to linearized equality constraints and an ellipsoidal trust region. Iterates must remain in the interior of the bound inequalities, but need not satisfy equality constraints until convergence. The algorithm reduces to the primal barrier interior point method for linear programming problems. In the past two years M. Lalee, Nocedal and Plantenga have implemented the Byrd-Omojokun algorithm for solving large-scale equality constrained problems using trust regions, and with this software test results have been obtained for the new interior point algorithm.
- OSTI ID:
- 36393
- Report Number(s):
- CONF-9408161--
- Country of Publication:
- United States
- Language:
- English
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A trust region method for nonlinear programming based on primal interior point techniques
A trust region method for nonlinear programming based on primal interior-point techniques