-double (*func_f_def)(const s_lmm_variable_t&, double);
-double (*func_fp_def)(const s_lmm_variable_t&, double);
-double (*func_fpi_def)(const s_lmm_variable_t&, double);
-
-/*
- * Local prototypes to implement the Lagrangian optimization with optimal step, also called dichotomy.
- */
-// solves the proportional fairness using a Lagrangian optimization with dichotomy step
-void lagrange_solve(lmm_system_t sys);
-// computes the value of the dichotomy using a initial values, init, with a specific variable or constraint
-static double dichotomy(double init, double diff(double, void*), void* var_cnst, double min_error);
-// computes the value of the differential of constraint param_cnst applied to lambda
-static double partial_diff_lambda(double lambda, void* param_cnst);