BT

Minimization of nonsmooth, locally Lipschitz functions subject to simple constraints.

All algorithms are based on a combination of the bundle concept developed for the minimization of locally Lipschitz, weakly semismooth functions and the trust region philosophy, now widely used in optimization. For the solution of inner quadratic programming problems, an algorithm due to Powell is used.

The software is written in Fortran 77 in double precision. A common-block /CMACHE/EPS must be provided by the user in subroutine QL0001, where EPS defines the underlying machine precision. The user must also provide a subroutine for computing the objective function and an arbitrary subgradient at any admissible point.

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Contact:

Prof. Dr. J. Zowe                  Dr. J. V. Outrata 
Chair of Applied Mathematics II    Inst. of Information Theory & Automatization
University of Erlangen-Nuremberg   Czech Academy of Sciences
D-91058 Erlangen                   Pod vodarenskou vezi 4
Germany                            CZ-18208 Prague 8
Phone: +49 (913) 185-7509          Czech Republic
Fax: +49 (913) 185-8126
E-Mail: zowe@am.uni-erlangen.de    outrata@utia.cas.cz

References

C. Lemarechal, J.-J. Strodiot, and A. Bihain, On a bundle algorithm for nonsmooth optimization, in Nonlinear Programming 4, O. L. Mangasarian, R. R. Meyer, and S. M. Robinson, eds., Academic Press, New York, 1991.

J. Outrata, J. Zowe, and H. Schramm, Bundle trust methods: Fortran codes for nondifferentiable optimization, User's Guide, DFG Report No. 269, 1991.

H. Schramm, J. Zowe, A version of the bundle idea for minimizing a nonsmooth function: conceptual idea, convergence analysis, numerical results, SIAM J. Optim. 2 (1992), pp. 121--152.

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