JSL Syntax Reference • JSL Functions • Optimization Functions
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Optimization Functions
Constrained Maximize(expr, {x1(low1, up1), x2(low2, up2), ...}, messages)
Description
Finds the values for the x arguments, specified as a list, that maximize the expr expression with optional linear constraints. You must specify lower and upper bounds in parentheses for each argument.
In the following messages, A is a matrix of coefficients. x = [x1, x2, ...] is the vector of arguments. b is a vector that forms the right side of the expression.
Messages
<<Less than EQ({A, b})
Sets the constraint to less than or equal to the specified values (A*x <= b).
<<Greater Than EQ({A, b})
Sets the constraint to greater than or equal to the specified values (A*x >= b).
<<Equal To({A, b})
Sets the constraint as equal to the specified values (A*x = b).
<<Starting Values([x1Start, x2Start, ...])
Specifies a starting point.
<<Max Iter(int)
An integer that specifies the maximum number of iterations to be performed.
<<Tolerance(p)
p sets the tolerance for the convergence criterion. The default tolerance is 10^5.
<<Show Details("true")
Returns a list with the final values for (objective value, number of iterations, gradient, and Hessian). Shows the step-by-step results of the optimizer in the log.
Constrained Minimize(expr, {x1(low1, up1), x2(low2, up2), ...}, messages)
Description
Finds the values for the x arguments, specified as a list, that minimize the expr expression with optional linear constraints. You must specify lower and upper bounds in parentheses for each argument.
In the following messages, A is a matrix of coefficients. x = [x1, x2, ...] is the vector of arguments. b is a vector that forms the right side of the expression.
Messages
<<Less than EQ({A, b})
Sets the constraint to less than or equal to the specified values (A*x <= b).
<<Greater Than EQ({A, b})
Sets the constraint to greater than or equal to the specified values (A*x >= b).
<<Equal To({A, b})
Sets the constraint as equal to the specified values (A*x = b).
<<Starting Values([x1Start, x2Start, ...])
Specifies a starting point.
<<Max Iter(int)
An integer that specifies the maximum number of iterations to be performed.
<<Tolerance(p)
p sets the tolerance for the convergence criterion. The default tolerance is 10^5.
<<Show Details("true")
Returns a list with the final values for (objective value, number of iterations, gradient, and Hessian). Shows the step-by-step results of the optimizer in the log.
Desirability(yVector, desireVector, y)
Description
Fits a function to go through the three points, suitable for defining the desirability of a set of response variables (y’s). yVector and desireVector are matrices with three values, corresponding to the three points defining the desirability function. The actual function depends on whether the desire values are in the shape of a larger-is-better, smaller-is-better, target, or antitarget.
Returns
The desirability function.
Arguments
yVector
Three input values.
desireVector
the corresponding three desirability values.
y
the value of which to calculate the desirability.
LPSolve(A, b, c, L, U, neq, nle, nge, <slackVars(Boolean)>)
Description
Returns a list containing the decision variables (and slack variables if applicable) in the first list item and the optimal objective function value (if one exists) in the second list item.
Arguments
A
A matrix of constraint coefficients.
b
A matrix that is a column of right hand side values of the constraints.
c
A vector of cost coefficients of the objective function.
L, U
Matrices of lower and upper bounds for the variables.
neq
The number of equality constraints.
nle
The number of less than or equal inequalities.
nge
The number of greater than or equal inequalities.
slackVars(Boolean)
Optional. Determines whether the slack variables are returned in addition to the decision variables. The default value is 0.
Note
The constraints must be listed as equalities first, less than or equal inequalities next, and greater than or equal inequalities last.
Maximize(expr, {x1(low1, up1), x2(low2, up2), ...}, messages)
Description
Finds the values for the x arguments, specified as a list, that maximize the expression expr. You can specify lower and upper bounds in parentheses for each argument. Additional arguments for the function enable you to set the maximum number of iterations, tolerance for convergence, and view more details about the optimization. The Newton-Raphson method is used when an analytical derivative is found for the Hessian. Otherwise, the Symmetric-Rank One method (SR1), a quasi-Newton method, is used.
Messages
<<Max Iter(int)
An integer that specifies the maximum number of iterations to be performed.
<<Tolerance(p)
p sets the tolerance for the convergence criterion. The default tolerance is 10^-8.
<<Show Details("true")
Returns a list with the final values for the objective value, number of iterations, gradient, and Hessian. Shows the step-by-step results of the optimizer in the log.
Minimize(expr, {x1(low1, up1), x2(low2, up2), ...}, messages)
Description
Finds the values for the x arguments, specified as a list, that minimize the expression expr. You can specify lower and upper bounds in parentheses for each argument. Additional arguments for the function enable you to set the maximum number of iterations, tolerance for convergence, and view more details about the optimization. The Newton-Raphson method is used when an analytical derivative is found for the Hessian. Otherwise, the Symmetric-Rank One method (SR1), a quasi-Newton method, is used.
Messages
<<Max Iter(int)
An integer that specifies the maximum number of iterations to be performed.
<<Tolerance(p)
p sets the tolerance for the convergence criterion. The default tolerance is 10^-8.
<<Show Details("true")
Returns a list with the final values for the objective value, number of iterations, gradient, and Hessian. Shows the step-by-step results of the optimizer in the log.

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Help created on 7/12/2018