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Numerische Mathematik

, Volume 54, Issue 5, pp 507–531 | Cite as

A decomposition-dualization approach for solving constrained convex minimization problems with applications to discretized obstacle problems

  • Michael Krätzschmar
Article

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 byH-matrices. Numerical tests for solving obstacle problems in ℝ1 discretized by using piecewise quadratic finite elements and in ℝ2 by using the five-point difference approximation are presented.

Subject Classifications

AMS(MOS):65K10, 65N20, 90C25 CR:G1.6 

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Copyright information

© Springer-Verlag 1989

Authors and Affiliations

  • Michael Krätzschmar
    • 1
  1. 1.Technische Hochschule DarmstadtDarmstadtFederal Republic of Germany

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