Variable Metric Methods for Constrained Optimization

Variable metric methods solve nonlinearly constrained optimization problems, using calculated first derivatives and a single positive definite matrix, which holds second derivative information that is obtained automatically. The theory of these methods is shown by analysing the global and local convergence properties of a basic algorithm, and we find that superlinear convergence requires less second derivative information than in the unconstrained case. Moreover, in order to avoid the difficulties of inconsistent linear approximations to constraints, careful consideration is given to the calculation of search directions by unconstrained minimization subproblems. The Maratos effect and relations to reduced gradient algorithms are studied briefly.