The tool solver_opt computes the goblal minimun and the minimizers of a polynomial function in a basic semialgebraic set, when there is a finite number of minimizers.
![\[ inf f(x) s.t. g_1(x)=0,\ldots,g_{n_1}(x)=0,h_1(x)\ge 0,\ldots,h_{n_2}(x)\ge 0 \]](form_0.png)
It can be used as follows:
where expl is a file containing the data of the minimization problem. The structure of the data file is the following:
1 n1 n2
f;
g_i;
...
h_j;
...
where
- n1 is the number of equalities,
- n2 is the number of inequalities,
- f is the polynomial to optimize,
- g_i are the equality constraints,
- h_j are the inequality constraints.
Here is an example with one polynomial function to optimize under zero equality constraint and 3 non-negativity constraints:
1 0 3
-10+2*x0+6*x1-2*x0^2+2*x0*x1-2*x1^2;
-x0^2+2*x0;
-8-x1^2+6*x1;
1-x0^2+2*x0*x1-x1^2;
The polynomials are separated by a ; The variables are x0, x1, … The output result is the dimension of the quotient space:
Number of solution(s): 1
Infimum: -3.0000000000
The infimum and an approximation of the minimizer(s) are stored in the file expl.sol:
sol:= [[0.1625682092242973109e1,0.2233710195183024716e1]];
fmin:= -0.3e1;
Options:
--help, -h : print this message
-s n : solver that you can use (1-
SDPA, 2-SDPAGMP, 3-CSDP, 4-MOSEK)
(1 by default)
-m n : use the method decomposer (0) or the full matrix method (1)
(0 by default)
-p f : use the
file f as parameter
file in the sdpa call
-t threshold : precise the threshold (1e-3 by default)
-b n : precise
if we use the complet border
basis (0 by
default) or not (1)
