RMPSolveS: Recursive Modified Pattern Search on Simplex

In RMPSS: Recursive Modified Pattern Search on Simplex

Description

'RMPSolveS' can be used to maximize any function where the set of parameters belong to an unit simplex.

Arguments

x0	Vector of Initial Guess provided by User.
func	The Function to be Optimized, should be provided by the User.
s_init	Initial 'Global Step Size'. Default Value is 2. It must be set Less than or Equal to 2.
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}.
max_iter	Max Number of Iterations in each 'Run'. Default Value is 10000.
no_runs	Max Number of 'Runs'. Default Value is 10^{-6}.
lambda	Sparsity Control Parameter. Default Value is 10^{-10}.
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}.
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
  "Recursive Modified Pattern Search on High-dimensional Simplex : A Blackbox Optimization Technique"
  (available at 'arXiv http://arxiv.org/abs/1604.08636).

Examples

g <- function(y)
return(-20 * exp(-0.2 * sqrt(0.5 * (y[1] ^ 2 + (y[2]-1) ^ 2)))
         - exp(0.5 * (cos(2 * pi * y[1]) + cos(2 * pi * (y[2]-1))))
         + exp(1) + 20)
         
# global min value is 0, achieved at c(0,1)

starting_point <- c(0.4,0.6)
         
g(starting_point)
solution <- RMPSolveS(starting_point, g)
g(solution)
           
# Example of putting infeasible starting point

g <- function(y)
return(-y[1])   # min value is 1, achieved if first coordinate is 1
             
RMPSolveS(c(1,0.2,56,0.4),g) # starting point NOT on simplex
               
               
# Example of 1000 dimensional problem
g <- function(y)
return(- sum(y^10))
                 
# min value is -1, achieved if only one
# coordinate is equal to 1, rest are 0

RMPSolveS(rep(1 / 1000, 1000), g, print = 1)

RMPSS documentation built on Aug. 12, 2020, 9:07 a.m.