Summary.In this paper, we shall be concerned with the solution of constrained convex minimization problems. The constrained convex minimization problems are proposed to be transformable into a convex-additively decomposed and almost separable form, e.g. by decomposition of the objective functional and the restrictions. Unconstrained dual problems are generated by using Fenchel-Rockafellar duality. This decomposition-dualization concept has the advantage that the conjugate functionals occuring in the derived dual problem are easily computable. Moreover, the minimum point of the primal constrained convex minimization problem can be obtained from any maximum point of the corresponding dual unconstrained concave problem via explicit return-formulas. In quadratic programming the decomposition-dualization approach considered here becomes applicable if the quadratic part of the objective functional is generated by H-matrices. Numerical tests for solving obstacle problems in lR x discretized by using piecewise quadratic finite elements and in IR 2 by using the five-point difference approximation are presented.
Monotone methods are applied to nonlinear operator equations in order to obtain sequences of upper and lower bounds for solutions. It is shown, that by relaxed regularity conditions to the ordering the sequences converge monotonically and superlinearly, too. The assumptions on the starting points are relaxed by consideration of different orderings in the range of the operator. The results are applied to mildly nonlinear boundary value problems.
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