SequentialLineMin: Minimize a function of r variables by sequential univariate...
In scdensity: Shape-Constrained Kernel Density Estimation

Description Usage Arguments Details Value Examples

The function seeks to minimize fcn, a scalar function of r variables. v0 is a starting solution and bounds is a 2-vector giving upper and lower limits for elements of the solution.

1	SequentialLineMin(fcn, bounds, v0, tol = .Machine$double.eps^0.25)

`fcn`	A function with taking an r-vector as its first argument: call as `fcn(v,...)`.
`bounds`	A 2-vector giving the upper and lower limits for elements of a solution.
`v0`	A starting solution, with increasing elements. An r-vector. Not used if r == 1.
`tol`	Tolerance passed to `optimize`.

This algorithm is designed to search for solutions of the form v = [v_1 v_2 … v_r], where bounds(1) < v_1 < v_2 < ... < v_r < bounds(2). It loops through the solution vector one variable at a time, and does a 1-D line search using optimize() for an improving value of that variable. So when optimizing v_i, it searches the interval (v_{i-1}, v_{i+1}) to maintain the increasing nature of v. The overall search terminates once a pass through all r elements of v fails to produce any changes to v.