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- Title
I-SMOOTH: Iteratively Smoothing Mean-Constrained and Nonnegative Piecewise-Constant Functions.
- Authors
Huifen Chen; Schmeiser, Bruce
- Abstract
Continuous nonnegative functions, such as Poisson rate functions, are sometimes approximated as piecewise-constant functions. We consider the problem of automatically smoothing such functions while maintaining the integral of each piece and maintaining nonnegativity everywhere, without specifying a parametric function. We develop logic for SMOOTH (Smoothing via Mean-constrained Optimized-Objective Time Halving), a quadratic-optimization algorithm that yields a smoother nonnegative piecewise-constant rate function having twice as many time intervals, each of half the length. I-SMOOTH (Iterated SMOOTH) iterates the SMOOTH formulation to create a sequence of piecewise-constant rate functions that, in the limit, yields a nonparametric continuous function. We consider two contexts: finite-horizon and cyclic. We develop a sequence of computational simplifications for SMOOTH, moving from numerically minimizing the quadratic objective function, to numerically computing a matrix inverse, to a closed-form matrix inverse obtained as finite sums, to optimal decision-variable values that are linear combinations of the given rates, and to simple approximations.
- Subjects
ITERATIVE methods (Mathematics); CONSTRAINT satisfaction; SMOOTHNESS of functions; NONPARAMETRIC estimation; CONTINUOUS functions; COMPUTATIONAL complexity; POISSON processes
- Publication
INFORMS Journal on Computing, 2013, Vol 25, Issue 3, p432
- ISSN
1091-9856
- Publication type
Article
- DOI
10.1287/ijoc.1120.0512