Gurobi (>= 8.1) 能否在 R 接口内解决具有二次等式约束的 ILP？

Question

来自这个问题的回答 here 3 年前看来，这是不可能的。 Gurobi 文档对我来说不是很清楚：

quadcon (optional)
...
The optional sense string defines the sense of the quadratic constrint. Allowed values are <, = or >. If not present, the default sense is <. It is stored in model$quadcon[[i]]$sense.

constraints 状态

Quadratic Constraints
...
Quadratic equality constraints are always non-convex; they will give a GRB_ERROR_QCP_EQUALITY_CONSTRAINT error with default settings.
[...] If you set the NonConvex parameter to 2, however, then Gurobi will accept arbitrary quadratic constraints and attempt to solve the resulting model.

但是 NonConvex 在 R 中抛出一个 Error 10007: Unknown parameter: 'NonConvex'。
感谢任何帮助，可以在下面找到可重现的示例：

library(Matrix)
model <- list(
  modelsense = "min", 
  Q = structure(c(1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1), .Dim = c(4L, 4L)), 
  A = structure(c(36, 0, 24, 0, -23, 0, -49, 1), .Dim = c(2L, 4L)), 
  rhs = c(0, 1), 
  sense = c("=", ">="), 
  vtype = "I", 
  quadcon = list(list(Qc = new("dgTMatrix", i = 0:3, j = 0:3, 
                              Dim = c(4L, 4L), 
                              Dimnames = list(NULL, NULL), 
                              x = c(1, 1, 1, -2), 
                              factors = list()),
                     # sense = "<=", # works fine
                     sense = ">=", # Error 10020: Q matrix is not positive semi-definite (PSD)
                     sense = "=", # Error 10021: Quadratic equality constraints
                     rhs = 0)))

params <- list(OutputFlag = 0)
result <- gurobi::gurobi(model, params)
print(result$x)

Answer 1

就像mattmilten在评论中已经说过的，有必要升级到9.0版本。然后它应该与

一起工作

params <- list(OutputFlag = 0, NonConvex = 2)

Gurobi (>= 8.1) 能否在 R 接口内解决具有二次等式约束的 ILP？

Can Gurobi (>= 8.1) solve ILP with quadratic equality constraint within R-interface?

r

gurobi