Specify the objective function as a procedure that accepts n floating-point parameters corresponding to the problem variables and returns a float.

The Optimization[LSSolve] command accepts an objective function of the form  $\left(\frac{1}{2}\right)\left({\mathrm{f1}\left(\mathrm{x1}\,\mathrm{x2}\,\mathrm{...}\,\mathrm{xn}\right)}^2+{\mathrm{f2}\left(\mathrm{x1}\,\mathrm{x2}\,\mathrm{...}\,\mathrm{xn}\right)}^2+\mathrm{...}+{\mathrm{fq}\left(\mathrm{x1}\,\mathrm{x2}\,\mathrm{...}\,\mathrm{xn}\right)}^2\right)$.  In this situation, the objective function is specified as a list of procedures, each taking $n$ floating-point parameters representing the problem variables and returning a float.  These procedures compute the least-squares residuals $\mathrm{f1}$, $\mathrm{f2}$, ..., $\mathrm{fq}$.

Specify the inequality constraints as a set or list of procedures.  A single constraint $v\left(\mathrm{x1}\,\mathrm{x2}\,\mathrm{...}\,\mathrm{xn}\right)\le 0$ is specified as a procedure v of the same form as the objective function previously described and returning the left-hand side value of the constraint.

Specify the equality constraints also as a set or list of procedures.  Each constraint $w\left(\mathrm{x1}\,\mathrm{x2}\,\mathrm{...}\,\mathrm{xn}\right)=0$ is specified as a procedure returning the left-hand side value of the constraint.

Specify bounds as a sequence of ranges.  For example, the sequence $\mathrm{-1.0}..2.5,0.5..3.2$ indicates that the first problem variable is constrained to be between $\mathrm{-1.0}$ and $2.5$, and the second is constrained to be between $0.5$ and $3.2$.  If bounds are provided, the number of ranges must be equal to the number of problem variables.

Bounds can be included with the general constraints. For example, adding the inequalities $1.5\le x$ and $x\le 3.2$ to the constraint set is equivalent to specifying $x=1.5..3.2$. Bounds are not required to be specified separately, though this usually leads to more efficient computation.

The problem variables are not assumed to be non-negative by default, but the $\mathrm{assume}=\mathrm{nonnegative}$ option can be used to specify this. For more information, see the Optimization/Options help page.

Specify the initial values using the option initialpoint=p, where p is a list of realcons.  The list must contain one value for each problem variable.  For more information on the initialpoint option, see the Optimization/Options help page.

Maple returns the solution as a list containing the final minimum (or maximum) value and a point (the computed extremum).  The point is a Vector containing the values of the problem variables unless the problem involves units in which case the point will be a list (see Optimization/General/Units).

$\mathrm{with}\left(\mathrm{Optimization}\right)$

$\left[\mathrm{ImportMPS}\,\mathrm{Interactive}\,\mathrm{LPSolve}\,\mathrm{LSSolve}\,\mathrm{Maximize}\,\mathrm{Minimize}\,\mathrm{NLPSolve}\,\mathrm{QPSolve}\right]$

p := proc(x)
  if x <= 0 then
    x^2+1;
  else
    sin(x)/x;
  end if;
end proc;

$p≔\mathbf{proc}\left(x\right)\mathbf{if}x<=0\mathbf{then}x\&Hat;2\&plus;1\mathbf{else}\sin \left(x\right)\&sol;x\mathbf{end\; if}\mathbf{end\; proc}$

$\mathrm{NLPSolve}\left(p\&comma;-5..30\right)$

$\left[\mathrm{-0.0424796169776126}\&comma;\left[\begin{array}{c}23.5194525091898\end{array}\right]\right]$

b1 := proc(x) x-1 end proc:

b2 := proc(x) x-7 end proc:

c1 := proc(x) -2*x-3 end proc:

c2 := proc(x) x-5 end proc:

$\mathrm{LSSolve}\left(\left[\mathrm{b1}\&comma;\mathrm{b2}\right]\&comma;\left\{\mathrm{c1}\&comma;\mathrm{c2}\right\}\&comma;1..10\right)$

$\left[9.00000000000000178\&comma;\left[\begin{array}{c}4.\end{array}\right]\right]$

$\mathrm{Maximize}\left(\left(x\&comma;y\right)\mapsto 3\cdot x^2+y\&comma;\left\{\left(x\&comma;y\right)\mapsto x-2\cdot y-2\&comma;\left(x\&comma;y\right)\mapsto y^2-x-3\right\}\&comma;\mathrm{initialpoint}=\left[5\&comma;5\right]\right)$

$\left[241.024997396375710\&comma;\left[\begin{array}{c}8.89897948556636\\ 3.44948974278318\end{array}\right]\right]$