Rsolnp:::solnp(pars = beta0, fun = lf,  eqfun = eq_constraint,
                                    ineqfun = positive_constraint,
                                    ineqLB = rep(0.001, length(beta0)),
                                    ineqUB = rep(Inf, length(beta0)),
                                    LB = rep(0.0001, length(beta0)),
                                    UB =rep(Inf, length(beta0)),
                                    control= list(trace = 1))