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Extra resources for A Bundle Algorithm Applied to Bilevel Programming Problems with Non-Unique Lower Level Solutions

Example text

2 contains the time after which the corresponding method no longer works. 0 GHz PC using CYGWIN. Additionally, the interval enclosures of the two angles ψ1 and ψ2 of the double pendulum are shown for identical time intervals in Fig. 5. The state enclosures obtained with TMoValenciaIntegrator are tighter than those of TMoAWAIntegrator towards the end of the integration interval. Actually, the use of the former integrator reduces overestimation of the resulting interval boxes up to 839 times for this example, cf.

Besides, an interesting point would be to study the influence of modeling on the solution, that is, how the performance of S MART MOBILE depends on the number of transmission elements and variables for the same mechanical system. As a further improvement of the efficiency of VAL E NC IA-IVP, an exclusion strategy for subintervals resulting from overestimation will be implemented which is based on a consistency test by backward integration of parts of the validated state enclosures determined by the present version of this program [RAH06].

Error handler, 2. Additional (non-basic) interval arithmetic features, 3. Vectors and matrix classes, 4. Level 1 and level 2 BLAS, 5. Automatic differentiation, 6. Taylor model arithmetic, and 7. Constraint propagation. Level 2 – Problem-solving routines: Chapter contents will initially mirror the contents of many numerical analysis texts, and will grow with time. 1. Linear systems, eventually including sparse and eigensystems, 2. Nonlinear systems, 3. Optimization, 4. Quadrature, 5. Statistics, 6.

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A Bundle Algorithm Applied to Bilevel Programming Problems with Non-Unique Lower Level Solutions by Dempe S.

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