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| Syntax |
dnlsqb(function fval, xini, xlow, xup, delta, maxit, level) |
| See Also | nlsqbox , linlsqb |
minimize |f(x)|^2 with respect to x
such that xlow <= x <= xup
dnlsqb is a value of x
that approximates the solution of the optimization problem.
The return value has the same type and dimension as xini.
(x, f_out)
and (x, f_out, df_out)
evaluate f(x) and its derivative.
The vector x has the same type and dimension as xini.
It specifies the point at which to evaluate f(x).
The input value of f_out does not matter.
Its output value is f(x)
as a column vector with the same type as x.
If df_out is present, its input value does not matter.
Its output value is the derivative of f(x)
as a matrix with the same type and row dimension as
f_out, and column dimension equal to the
row dimension of x.
The element df_out(i, j)
is the derivative of the i-th component of
f(x) with respect to the
j-th component of x.
|x(i) - xmin(i)| < delta * (xup(i) - xlow(i))
|f(x)|^2 is less than delta times its value.
The integer scalar maxit
specifies the maximum number of iterations to try
before giving up on convergence.
dnlsqb.
If dnlsqb fails to converge, the message
"dnlsqb failed to converge" is printed.
If level > 1,
the messages "begin dnlsqb" is printed before the first iteration
and if the method converges, "dnlsqb converged" is printed at the end.
In addition, the value of |f(x)|^2 is printed at each iteration.
If level > 2,
the value of x is printed at each iteration.
minimize [exp(x(1)) - exp(1.)]^2 + [exp(x(2)) - exp(2.)]^2
with respect to x such that
-1 < x(1) < +1
-1 < x(2) < +1
x(1) = 1 and
x(2) = 1.
clear
function fval(x, f_out, df_out) begin
f_out = {exp(x(1)) - exp(1.), exp(x(2)) - exp(2.)}
if arg(0) >= 3 then ...
df_out = diag(exp(x))
end
xini = { 0., 0.}
xlow = { -1., -1.}
xup = { +1., +1.}
delta = 1e-4
maxit = 10
level = 2
argmin = dnlsqb(function fval, xini, xlow, xup, delta, maxit, level)
print "argmin' =", argmin'