CMLS-package: Constrained Multivariate Least Squares

In CMLS: Constrained Multivariate Least Squares

Constrained Multivariate Least Squares

Description

Solves multivariate least squares (MLS) problems subject to constraints on the coefficients, e.g., non-negativity, orthogonality, equality, inequality, monotonicity, unimodality, smoothness, etc. Includes flexible functions for solving MLS problems subject to user-specified equality and/or inequality constraints, as well as a wrapper function that implements 24 common constraint options. Also does k-fold or generalized cross-validation to tune constraint options for MLS problems. See ten Berge (1993, ISBN:9789066950832) for an overview of MLS problems, and see Goldfarb and Idnani (1983) <doi:10.1007/BF02591962> for a discussion of the underlying quadratic programming algorithm.

Details

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The cmls function provides a user-friendly interface for solving the MLS problem with 24 common constraint options (the const function prints or returns the different contraint options). The cv.cmls function does k-fold or generalized cross-validation to tune the constraint options of the cmls function. The mlsei function solves the MLS problem subject to user-specified equality and/or inequality (E/I) constraints on the coefficients. The mlsun function solves the MLS problem subject to unimodality constraints and user-specified E/I constraints on the coefficients.

Author(s)

Nathaniel E. Helwig <[e-mail]>

Maintainer: Nathaniel E. Helwig <[e-mail]>

References

Goldfarb, D., & Idnani, A. (1983). A numerically stable dual method for solving strictly convex quadratic programs. Mathematical Programming, 27, 1-33. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1007/BF02591962")}

Helwig, N. E. (in prep). Constrained multivariate least squares in R.

Ten Berge, J. M. F. (1993). Least Squares Optimization in Multivariate Analysis. Volume 25 of M & T Series. DSWO Press, Leiden University. ISBN: 9789066950832

Turlach, B. A., & Weingessel, A. (2019). quadprog: Functions to solve Quadratic Programming Problems. R package version 1.5-8. https://CRAN.R-project.org/package=quadprog

Examples

# See examples for cmls, cv.cmls, mlsei, and mlsun

CMLS documentation built on April 3, 2023, 5:24 p.m.