constrOptim() 使用线性不等式约束并通过ui %*定义可行域% 参数 - ci >= 0.如果约束是 3 * d1 + d2 ，ui 是 c(-3, -1) 和 ci 是 -280.



constrOptim() uses linear inequality constraints and defines the feasible region by ui %*% param - ci >= 0. If the constraint is 3 * d1 + d2 <= 280, ui is c(-3, -1) and ci is -280.

Fd <- function(betas) {
    b1 = betas[1]
    b2 = betas[2]
   (224 * b1 + 84 * b2 + b1 * b2 - 2 * b1^2 - b2^2)
}

theta = c(59.999,100)    # because of needing " ui %*% inital_par - ci > 0 "
ui = c(-3, -1)
ci = -280                # those ui & ci mean " -3*par[1] + -1*par[2] + 280 >= 0 "

constrOptim(theta, Fd, NULL, ui = ui, ci = ci, control=list(fnscale=-1))
  # $par
  # [1] 69.00002 72.99993

如果你想要的不是不等式而是等式约束，***使用 Rsolnp 或 alabama 包.他们可以使用不等式和/或等式约束(参见用于等式和不等式约束的约束优化库).

If you want not inequality but equality constraints, it would be better to use Rsolnp or alabama package. They can use inequality and/or equality constraints (see Constrained Optimization library for equality and inequality constraints).

library(Rsolnp); library(alabama); 

Fd2 <- function(betas) {     #  -1 * Fd
   b1 = betas[1]
   b2 = betas[2]
   -1 * (224 * b1 + 84 * b2 + b1 * b2 - 2 * b1^2 - b2^2)
}

eqFd <- function(betas) {  # the equality constraint
    b1 = betas[1]
    b2 = betas[2]
    (3 * b1 + b2 -280)
}

solnp(pars = c(60, 100), fun = Fd2, eqfun = eqFd, eqB = 0)
auglag(par = c(60, 100), fn = Fd2, heq = eqFd)