A number of applications arising in chemical engineering, power engineering, PDE-constrained optimization are naturally stated as constrained nonlinear systems. In particular, systems where the variables are subjected to lower and upper bounds are fairly general because sets of algebraic equations and inequalities and the Karush-Kuhn-Tucker (KKT) systems can be cast in such form.
In this talk we discuss the numerical solution of bound constrained nonlinear systems via trust-region affine-scaling methods and examine procedures for medium and large-scale problems. The methods presented apply the same strategy to enforce strict feasibility of each iterate and allow for both spherical and elliptical trust-regions, while they differ on the techniques to solve the linear systems and trust-region subproblems. Medium-scale algorithms solve the full-space trust-region problems and rely on matrix factorizations. On the other hand, large-scale algorithms are Newton-Krylov method embedded into global strategies. A new algorithm is presented where an inexact dogleg procedure is employed to obtain an approximate minimizer of the model within the trust-region and the feasible set. The method also allows a great deal of flexibility in specifying the scaling matrix used to handle the bounds. Quite general scaling matrices are allowed and several existing scaling matrices from the recent literature satisfy our requirements.
Several numerical experiments are provided that illustrate the performance of the algorithms for different type of problems. For large problems we show that the new inexact dogleg procedure improve the performance of this class of methods.
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