Abstract
Most data-driven scientific inference, qualitative, quantitative, and visual analytics involve formulating, understanding the behavior of, and optimizing objective (cost) functions. Presenting the mathematical foundations of representation and interrogation of diverse spectra of objective functions provides mechanisms for obtaining effective solutions to complex big data problems. (Multivariate) function optimization (minimization or maximization) is the process of searching for variables x1, x2, x3, …, xn that either minimize or maximize the multivariate cost function f(x1, x2, x3, …, xn). In this chapter, we will specifically discuss (1) constrained and unconstrained optimization; (2) Lagrange multipliers; (3) linear, quadratic and (general) non-linear programming; and (4) data denoising.
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References
Cortez, P. (2014) Modern Optimization with R, Springer, ISBN 3319082639, 9783319082639.
CRAN Optimization & Math Programming Site provides details about a broad range of R optimization functions.
Vincent Zoonekynd’s Optimization Blog http://zoonek.free.fr/blosxom/R/2012-06-01_Optimization.html.
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© 2018 Ivo D. Dinov
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Dinov, I.D. (2018). Function Optimization. In: Data Science and Predictive Analytics. Springer, Cham. https://doi.org/10.1007/978-3-319-72347-1_22
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DOI: https://doi.org/10.1007/978-3-319-72347-1_22
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