rpsg_solver: solves optimization problem using General (Text) Format of...

In PSGExpress: Portfolio Safeguard: Optimization, Statistics and Risk Management

Description

To solve optimization problem using PSG solvers it is necessary to prepare problem in General (Text) format. There are three main objects of PSG:

• Problem Statement. It is a character with description of optimization problem. This object must be created according to the rules of PSG General format.
  Problem statement for optimization problems with one constraint:
  
  (minimize|maximize)
  [<coef1>*]<PSG function obj 1>
  .........
  [<coefK>*]<PSG function obj K>
  Constraint:(<=|>=|==) <bound>
  [<coef1>*]<PSG function constr 1>
  .........
  [<coefK>*]<PSG function constr K>
  Box: (<=|>=|==) <bound>

• PSG Data Objects. Data for optimization problem in a specific format: PSG Matrix, PSG PMatrix, PSG Point, and PSG Vector.

• PSG Solution. The results of optimization problem are stored in solution report (character) and PSG Data Objects (PSG Matrix, PSG Point, ect).

Usage

rpsg_solver(problem_list, rho = parent.frame(), allowExt = TRUE,
  rpsg_suppress.Messages = FALSE)

Arguments

problem_list	list with data for optimization problem. List members: problem_list$problem_statement character with PSG Problem Statement; problem_list$matrix_<name> matrix with names of columns that correspond to names of optimization variables. Name of this list member (matrix_<name>) must correspond to the name of PSG Matrix in Problem Statement. Matrix may include two optional collumns: scenario_benchmark and scenario_probability; problem_list$pmatrix_<name> sparse matrix with names of columns that correspond to names of optimization variables. Name of this list member (pmatrix_<name>) must correspond to the name of PSG PMatrix in Problem Statement. PMatrix may include two optional collumns: scenario_benchmark and scenario_probability; problem_list$point_<name> vector with names of members that correspond to names of optimization variables. Name of this list member (point_<name>) must correspond to the name of PSG Point in Problem Statement; problem_list$vector_<name> vector with data. Name of this list member (vector_<name>) must correspond to the name of PSG Vector in Problem Statement.
rho	optional parameter for setting frame. Default is rho = parent.frame().
allowExt	optional parameter to specify if a solver can use variables from data frame defined in rho (by the default allowExt = TRUE) or not (allowExt = FALSE).
rpsg_suppress.Messages	optional parameter specifying if messages, that may appear when you run this function, should be suppressed (rpsg_suppress.Messages = TRUE) or not (by the default: rpsg_suppress.Messages = FALSE).

Value

list output.list with solution results:

output.list$problem_name

name (problem_<name>) of the optimization problem. By default: problem_1;

output.list$solution_status

status of solution of the optimization problem: optimal | feasible | infeasible | unbounded | calculated (for calculation problems);

output.list$problem_statement

Problem Statement of the solved problem;

output.list$output

solution report = character with main information about optimization results;

output.list$point_constraints_problem_<name>

optimal values of left hand sides of constraints in optimization problem;

output.list$point_slack_constraints_problem_<name>

slacks value for constraints of the optimization problem;

output.list$point_dual_constraints_problem_<name>

dual constraints values;

output.list$point_problem_<name>

optimal point for solved optimization problem;

output.list$log

information about solving process.

Note

• rpsg_solver supports two cases of input data:
  1. all PSG data objects are saved in input list,
  2. all PSG data objects are saved in Global Environment.
  In both cases input list must include PSG Problem Statement (problem_list$problem_statement) and names of PSG data objects (names of list members or variables) should be used in Problem Statement.

• Use rpsg_getsolution to convert character solution report into list witn numeric data.

• Use rpsg_verify to verify problem before optimization.

• List with solution results output.list may include output matrices, vectors and points not mentioned above. It is due to the specific of some PSG functions used in optimization problem.

Author(s)

Stan Uryasev [aut, cre, cph], Grigoriy Zrazhevsky [aut], Viktor Kuzmenko [aut], Alex Zrazhevsky [aut]

Maintainer: Stan Uryasev <[e-mail]>

References

American Optimal Decisions
Portfolio Safeguard Help

See Also

rpsg_verify rpsg_riskprog rpsg_getsolution

Examples

#Problem of CVaR minimization with constraint on the mean profit:
#Find x = (x1,x2,x3,x4) minimizing
#risk(x) = CVaR(0.95,x)
#subject to
#Average Gain(x)>4.5
#x1+x2+x3+x4 = 1
#x1>=0, x2>=0, x3>=0, x4>=0

matrix_scenarios <- matrix(c(1,4,8,3, 7,5,4,6, 2,8,1,0,0,3,4,9),nrow=4, byrow=TRUE)
colnames(matrix_scenarios) <- colnames(matrix_scenarios,do.NULL = FALSE, prefix = "x")
scenario_benchmark <- c(0.2, 0.11, 0.6, 0.1)
matrix_scenarios <- cbind(matrix_scenarios,scenario_benchmark)
matrix_budget <- matrix(c(1, 1, 1, 1),nrow=1)
colnames(matrix_budget) <- colnames(matrix_budget,do.NULL = FALSE, prefix = "x")
point_lowerbounds <- c(0, 0, 0, 0)
names(point_lowerbounds) <- rownames(point_lowerbounds,do.NULL = FALSE, prefix = "x")

# Case 1. PSG data is saved in list
problem_list <- list()

#Problem Statement
problem_list$problem_statement <- sprintf(
 "minimize
 cvar_risk(0.95,matrix_scenarios)
Constraint: >= 4.5
 avg_g(matrix_scenarios)
Constraint: == 1
 linear(matrix_budget)
Box: >= point_lowerbounds
Solver:CAR")

# PSG Matrix:
problem_list$matrix_scenarios <- matrix_scenarios

# PSG Matrix:
problem_list$matrix_budget <- matrix_budget

# PSG Point:
problem_list$point_lowerbounds <- point_lowerbounds

# Solve optimization problem
output.list.1 <- rpsg_solver(problem_list)

print(output.list.1)


# Case 2. PSG data is saved in Global Environment
problem_list <- list()

#Problem Statement
problem_list$problem_statement <- sprintf(
 "minimize
 cvar_risk(0.95,matrix_scenarios)
Constraint: >= 4.5
 avg_g(matrix_scenarios)
Constraint: == 1
 linear(matrix_budget)
Box: >= point_lowerbounds")

output.list.2 <- rpsg_solver(problem_list)

print(output.list.2)

PSGExpress documentation built on July 26, 2019, 5:02 p.m.