SCOptim {SCOR}

Spherically Constrained Optimization

Description

SCOptim runs our optimization algorithm, efficient in estimating maximizing Hyper Volume Under Manifolds Estimators.

Usage

SCOptim(
  x0,
  func,
  rho = 2,
  phi = 0.001,
  max_iter = 50000,
  s_init = 2,
  tol_fun = 1e-06,
  tol_fun_2 = 1e-06,
  minimize = TRUE,
  time = 36000,
  print = FALSE,
  lambda = 0.001,
  parallel = FALSE
)

Arguments

x0

The initial guess by user

func

The function to be optimized

rho

Step Decay Rate with default value 2

phi

Lower Bound Of Global Step Size. Default value is 10^{-6}

max_iter

Max Number Of Iterations In each Run. Default Value is 50,000.

s_init

Initial Global Step Size. Default Value is 2.

tol_fun

Termination Tolerance on the function value. Default Value is 10^{-6}

tol_fun_2

Termination Tolerance on the difference of solutions in two consecutive runs. Default Value is 10^{-6}

minimize

Binary Command to set SCOptim on minimization or maximization. TRUE is for minimization which is set default.

time

Time Allotted for execution of SCOptim

print

Binary Command to print optimized value of objective function after each iteration. FALSE is set fault

lambda

Sparsity Threshold. Default value is 10^{-3}

parallel

Binary Command to ask SCOptim to perform parallel computing. Default is set at FALSE.

Details

SCOptim is the modified version of RMPS, Recursive Modified Pattern Search. This is a blackbox algorithm efficient in optimizing non-differentiable functions. It works great in the shown cases of SHUM, EHUM and ULBA.

Value

The point where the value Of the Function is maximized under a sphere.

References

• Das, Priyam and De, Debsurya and Maiti, Raju and Chakraborty, Bibhas and Peterson, Christine B
  "Estimating the Optimal Linear Combination of Biomarkers using Spherically Constrained Optimization"
  (available at 'arXiv https://arxiv.org/abs/1909.04024).

Examples

f <- function(x)
return(x[2]^2 + x[3]^3 +x[4]^4)

SCOptim(rep(1,10), f)

SCOptim(c(2,4,6,2,1), f, minimize = FALSE, print = TRUE)
#Will Print the List and Find the Maximum

SCOptim(c(1,2,3,4), f, time = 10, lambda = 1e-2)
#Will perform no iterations after 10 secs, Sparsity Threshold is 0.01