RMPSS (version 1.1.1)

RMPSolveS: 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

# NOT RUN {
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
               
# }
# NOT RUN {
# 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)
# }
# NOT RUN {

# }