| Library: | nummath |
| See also: | nmsimpen |
| Quantlet: | nmqpenalty | |
| Description: | auxiliary quantlet for constrained minimization using nmsimpen. Computes a penalized function value: P(x,delta) = f(x) + delta*sum((constr(x))^2) |
| Usage: | pval = nmqpenalty(x) | |
| Input: | ||
| x | n x 1 vector, the point at which penalized function has to be evaluated | |
| nmlagrangianfname | global variable, string, name of the function to minimize. The function should have just one parameter x, which is either a n x 1 vector, or a n x k matrix (for any k >= 1) containing x = (x1,x2,...,xk); xi (n x 1 vector; i=1..k) represent points at which the function should be evaluated. As a result, the function should return a scalar or a 1 x k vector, respectively. | |
| nmlagrangiancname | global variable, string containing the name of a function evaluating equality constraints or a list containing at least one of nmlagrangiancname.eq and nmlagrangiancname.neq, both strings containing names of functions evaluating equality and inequality constraints, respectively. | |
| nmlagrangiandelta | global variable, scalar, penalization factor | |
| Output: | ||
| pval | scalar, value of penalized function | |
| nmlagrangianconstr | global variable, a list with elements nmlagrangianconstr.cvaleq and nmlagrangianconstr.cvalneq, containing values of penalized constraints, i.e., cvaleq = eq(x) and cvalneq = -min(0 | neq(x)) | |
If nmlagrangiancname is a string, a problem with only equality constraints (evaluated by nmlagrangiancname) is considered.
Inequality constraints should be defined so that cneq(x) >= 0 in a feasible set.
library("nummath")
proc(fval)=ftion(x)
fval = x[1,]^2 + x[1,].*x[2,] - 1
endp
proc(cval)=constr(x)
cval = x[1,] + x[2,]^2 - 2
endp
nmlagrangianfname = "ftion"
nmlagrangiancname = "constr"
nmlagrangiandelta = 10
putglobal("nmlagrangianfname")
putglobal("nmlagrangiancname")
putglobal("nmlagrangiandelta")
nmqpenalty(#(0,0))
Contents of pval [1,] 39
library("nummath")
proc(fval) = ftion(x)
fval = x[1,]^2 + x[1,].*x[2,] - 1
endp
; equality constraint: x1 + x2^2 = 2
proc(cval) = ceq(x)
cval = x[1,] + x[2,]^2 - 2
endp
; inequality constraint: x1 <= 0, i.e., -x1 >= 0
proc(cval) = cneq(x)
cval = -x[1,]
endp
nmlagrangianfname = "ftion"
eq = "ceq"
neq = "cneq"
nmlagrangiancname = list(eq,neq)
nmlagrangiandelta = 10
putglobal("nmlagrangianfname")
putglobal("nmlagrangiancname")
putglobal("nmlagrangiandelta")
nmqpenalty(#(2,1))
Contents of pval [1,] 55