Module: ppl/ppl Branch: master Commit: 65156364caa2da7235862998930736ca27c83236 URL: http://www.cs.unipr.it/git/gitweb.cgi?p=ppl/ppl.git;a=commit;h=65156364caa2d...

Author: François Galea francois.galea@uvsq.fr Date: Tue Mar 9 20:28:29 2010 +0100

Added two paragraphs about uses of the big parameter in the documentation.

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src/PIP_Problem.defs.hh | 35 ++++++++++++++++++++++++++++++++++- 1 files changed, 34 insertions(+), 1 deletions(-)

diff --git a/src/PIP_Problem.defs.hh b/src/PIP_Problem.defs.hh index 0f29afb..4def1e5 100644 --- a/src/PIP_Problem.defs.hh +++ b/src/PIP_Problem.defs.hh @@ -316,7 +316,40 @@ operator<<(std::ostream& s, const PIP_Problem& p); will be defined in terms of all the parameters (problem parameters and artificial parameters defined along the path).

- FIXME: different uses of the big parameter. + \par Solving maximization problems + You can solve a lexicographic maximization problem by reformulating its + constraints using variable substitution. Proceed the following steps: + - Create a big parameter (see PIP_Problem::set_big_parameter_dimension), + which we will call \f$M\f$. + - Reformulate each of the maximization problem constraints by + substituting each \f$x_i\f$ variable with an expression of the form + \f$M-x'_i\f$, where the \f$x'_i\f$ variables are to be minimized. + - Solve the lexicographic minimum for the \f$x'\f$ variable vector. + - In the solution expressions, substitute each \f$x'_i\f$ variable back + to \f$M-x_i\f$. + + You can choose to maximize only a subset of the variables while minimizing + the other variables. In that case, just apply the variable substitution + method on the variables you want to be maximized. The variable + optimization priority will still be in lexicographic order. + + \par Allowing variables to be arbitrarily signed + You can deal with arbitrarily signed variables by reformulating the + constraints using variable substitution. Proceed the following steps: + - Create a big parameter (see PIP_Problem::set_big_parameter_dimension), + which we will call \f$M\f$. + - Reformulate each of the maximization problem constraints by + substituting each \f$x_i\f$ variable with an expression of the form + \f$M+x'_i\f$, where the \f$x'_i\f$ variables are positive. + - Solve the lexicographic minimum for the \f$x'\f$ variable vector. + - In the solution expressions, substitute each \f$x'_i\f$ variable back + to \f$x_i-M\f$. + + You can choose to define only a subset of the variables to be + sign-unrestricted. In that case, just apply the variable substitution + method on the variables you want to be sign-unrestricted. + + FIXME: Solving problems with arbitrarily signed parameters */ class Parma_Polyhedra_Library::PIP_Problem { public: