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STRUCTURE-PRESERVING FUNCTION APPROXIMATION VIA CONVEX OPTIMIZATION
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DOI：10.1137/19M130128X.png)
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摘要
En 中文
Approximations of functions with finite data often do not respect certain structural properties of the functions. For example, if a given function is nonnegative, a polynomial approximation of the function is not necessarily also nonnegative. We propose a formalism and algorithms for preserving certain types of such structure in function approximation. In particular, we consider structure corresponding to a convex constraint on the approximant (for which positivity is one example). The approximation problem then converts into a convex feasibility problem, but the feasible set is relatively complicated so that standard convex feasibility algorithms cannot be directly applied. We propose and discuss different algorithms for solving this problem. One of the features of our machinery is flexibility: Relatively complicated constraints, such as simultaneously enforcing positivity, monotonicity, and convexity, are fairly straightforward to implement. We demonstrate the success of our algorithm on several problems in univariate function approximation.
Keyword:
structure-preserving approximation
high-order accuracy
convex optimization
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