Isotone optimization can be formulated as a convex programming problem with simple linear constraints.
This functions offers active set strategies for a collection of isotone optimization problems pre-specified in the
package.
Matrix with 2 columns that contains isotonicity conditions, i.e. for row i it holds that fitted value i column 1 <= fitted value i column 2 (see examples)
mySolver
Various functions are pre-defined (see details). Either to funtction name or the corresponding string equivalent can be used. For user-specified functions fSolver with additional
arguments can be used (see details as well).
x0
Feasible starting solution. If NULL the null-vector is used internally.
ups
Upper boundary
check
If TRUE, KKT feasibility checks for isotonicity of the solution are performed
maxiter
Iteration limit
...
Additional arguments for the various solvers (see details)
Details
The following solvers are specified. Note that y as the vector of observed values and weights as the vector of weights need to provided through ... for each solver (except for fSolver() and sSolver()). Some solvers need additional arguments as described in the corresponding solver help files. More technical details can be found in the package vignette.
The pre-specified solvers are the following (we always give the corresponding string equivalent in brackets):
lsSolver() ("LS") for least squares with diagonal weights, aSolver() ("asyLS") for asymmetric least squares, dSolver() ("L1") for the least absolute value, eSolver() ("L1eps") minimizes l1-approximation. hSolver() ("huber") for Huber loss function, iSolver() ("SILF") for SILF loss (support vector regression), lfSolver() ("GLS") for general least squares with non-diagonal weights, mSolver() ("chebyshev") for Chebyshev L-inf norm, oSolver() ("Lp") for L-p power norm, pSolver() ("quantile") for quantile loss function, and finally sSolver() ("poisson") for Poisson likelihood.
fSolver() for user-specified arbitrary differentiable functions. The arguments fobj (target function ) and gobj (first derivative) must be provided plus any additional arguments used in the definition of fobj.
Value
Generates an object of class activeset.
x
Vector containing the fitted values
y
Vector containing the observed values
lambda
Vector with Lagrange multipliers
fval
Value of the target function
constr.vals
Vector with the values of isotonicity constraints
Alambda
Constraint matrix multiplied by lambda (should be equal to gradient)
gradient
Gradient
isocheck
List containing the KKT checks for stationarity, primal feasibility, dual feasibility, and complementary slackness (>= 0 means feasible)
niter
Number of iterations
call
Matched call
Author(s)
Jan de Leeuw, Kurt Hornik, Patrick Mair
References
de Leeuw, J., Hornik, K., Mair, P. (2009). Isotone optimization in R: Active Set methods and pool-adjacent-violators algorithm.
Journal of Statistical Software, 32(5), 1-24.