Summary
The paper contains new results as well as surveys on recent developments on the constrained best interpolation problem, and in particular on the convex best interpolation problem. Issues addressed include theoretical reduction of the problem to a system of nonsmooth equations, nonsmooth analysis of those equations and development of Newton’s method, convergence analysis and globalization. We frequently use the convex best interpolation to illustrate the seemingly complex theory. Important techniques such as splitting are introduced and interesting links between approaches from approximation and optimization are also established. Open problems related to polyhedral constraints and strips may be tackled by the tools introduced and developed in this paper.
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Qi, HD. (2005). Some Theoretical Aspects of Newton’s Method for Constrained Best Interpolation. In: Jeyakumar, V., Rubinov, A. (eds) Continuous Optimization. Applied Optimization, vol 99. Springer, Boston, MA. https://doi.org/10.1007/0-387-26771-9_2
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DOI: https://doi.org/10.1007/0-387-26771-9_2
Publisher Name: Springer, Boston, MA
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