RMPSolveH {RMPSH}

Recursive Modified Direct Search on Hyper-rectangle

Description

'RMPSolveH' can be Used to Minimize any Non-Convex Blackbox Function where Each Parameter has an Upper Bound and Lower Bound.

Usage

RMPSolveH(
  x0,
  func,
  lb,
  ub,
  rho_1 = 2,
  rho_2 = 2,
  phi = 1e-06,
  no_runs = 1000,
  max_iter = 10000,
  s_init = 2,
  tol_fun = 1e-06,
  tol_fun_2 = 1e-20,
  max_time = 36000,
  print_output = FALSE
)

Arguments

x0

Vector of Initial Guess provided by User.

func

The Function to be Optimized, should be provided by the User.

lb

Vector of Lower Bounds, of same Dimension as 'x0'.

ub

Vector of Upper Bound, of same Dimension as 'x0'

rho_1

'Step Decay Rate' for the First Run Only (Default is 2).

rho_2

'Step Decay Rate' for Second Run Onwards (Default is 2).

phi

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

no_runs

Max Number of 'Runs'. Default Value is 1000.

max_iter

Max Number of Iterations in each 'Run'. Default Value is 10000.

s_init

Initial 'Global Step Size'. Default Value is 2. It must be set Less than or Equal to 2.

tol_fun

Termination Tolerance on when to decrease the 'Global Step Size'. Default Value is 10^{-6}. For more accuracy, user may set it to a Smaller Value e.g., 10^{-20}. However, for Expensive Objective Functions, for Faster Computation, User should set it to a Larger Value e.g, 10^{-3}.

tol_fun_2

Termination Tolerance on the Difference of Norms of solution points in two Consecutive Runs. Default Value is 10^{-20}. However, for Expensive Objective Functions, for Faster Computation, user should set it to a Larger Value e.g, 10^{-6}.

max_time

Time Alloted (In Seconds) for Execution of RMPSH. Default is 36000 secs (10 Hours).

print_output

Binary Command to Print Optimized Value of Objective Function after Each Iteration. Default is set as FALSE.

Value

The Optimal Solution Point.

References

• Das, Priyam
  "Black-box optimization on hyper-rectangle using Recursive Modified Pattern Search and application to ROC-based Classification Problem"
  (available at 'arXiv http://arxiv.org/abs/1604.08616).

Examples

g <- function(y)
 return(-20 * exp(-0.2 * sqrt(0.5 * (y[1] ^ 2 + y[2] ^ 2))) -
 exp(0.5 * (cos(2 * pi * y[1]) + cos(2 * pi * y[2]))) + exp(1) + 20)

starting_point <- rep(1, 10)

g(starting_point)

solution <- RMPSolveH(starting_point, g, rep(-33, 10), rep(33, 10))

g(solution)

RMPSolveH(c(2, 4, 6, 2, 1), g, rep(-3, 5), rep(23, 5), print_output = TRUE)
# Will Print the Updates after Each Iteration


g <- function(y)
 return(sum(y ^ 2))
RMPSolveH(rep(2.3, 100),
          g,
          rep(-11, 100),
          rep(13, 100),
          max_time = 2,
          print = 1)
# Will Exit and Return Result after 2 Seconds