Two-Phase Algorithm for Nonlinear Constraint Problems.

摘要

An algorithm is described which solves the general nonlinear programming problem with nonlinear constraints. The computational implementation is based on the iterative use of any available package which solves the linearly constrained problem with a nonlinear objective function. Large, sparse problems with nonlinear constraints can be solved by this algorithm, provided a suitable linear constraint package is used. The algorithm consits of two phases. The first (Phase I) uses an external squared penalty function to find a point x(1), close to a local minimum. Starting with x(1), the algorithm then solves a sequence of linearly constrained problems (Phase II). Selected nonlinear constraints are linearized for each such Phase II iteration. With suitable assumptions, convergence from any initial point, with quadratic convergence in Phase II, is shown. The practical implementation of this algorithm is described, and its potential application to a model for the assessment of energy alternatives is discussed briefly. (Author)