Qi, Hou-Duo and Yang, Xiaoqi.Q.
Regularity and well-posedness of a dual program for
convex best C1-spline interpolation
Computational Optimization and Applications, 37, . (doi:10.1007/s10589-007-9027-y).
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An efficient approach to computing the convex best C1-spline interpolant
to a given set of data is to solve an associated dual program by standard numerical
methods (e.g., Newton’s method). We study regularity and well-posedness of the
dual program: two important issues that have been not yet well-addressed in the literature.
Our regularity results characterize the case when the generalized Hessian of the
objective function is positive definite. We also give sufficient conditions for the coerciveness
of the objective function. These results together specify conditions when
the dual program is well-posed and hence justify why Newton’s method is likely to
be successful in practice. Examples are given to illustrate the obtained results.
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