JuMP+NLopt优化失败，不报错只返回初值

综合讨论区 库的安装及使用
1

9个参数的非线性优化问题，调用Ipopt没问题，调用NLopt不报错但只返回初始值。由于相同操作要重复几万次，但Ipopt不是thread-safe，所以最终还是想用NLopt实现。请教下哪里出错了？

NLopt版本：

using JuMP
using NLopt
using LinearAlgebra
ask()
function ask()
    lb = [-1, -1, -1, -1, -1, -1, -1, -1, -1]
    ub = [ 1,  1,  1,  1,  1,  1,  1,  1,  1]
    x0 = [0.7, 0.7, 0.07, -0.4, 0.5, -0.7, -0.5, 0.5, 0.7]

    model = Model(NLopt.Optimizer)
    set_optimizer_attribute(model, "algorithm", :LD_SLSQP)
    @variable(model, lb[1] ≤ x1 ≤ ub[1], start = x0[1])
    @variable(model, lb[2] ≤ x2 ≤ ub[2], start = x0[2])
    @variable(model, lb[3] ≤ x3 ≤ ub[3], start = x0[3])
    @variable(model, lb[4] ≤ x4 ≤ ub[4], start = x0[4])
    @variable(model, lb[5] ≤ x5 ≤ ub[5], start = x0[5])
    @variable(model, lb[6] ≤ x6 ≤ ub[6], start = x0[6])
    @variable(model, lb[7] ≤ x7 ≤ ub[7], start = x0[7])
    @variable(model, lb[8] ≤ x8 ≤ ub[8], start = x0[8])
    @variable(model, lb[9] ≤ x9 ≤ ub[9], start = x0[9])

    @NLobjective(model, Min, x1^2+x2+x3^2+x4+x5^2+x6+x7^2+x8+x9^2)
    @constraint(model, [x1 x2 x3; x4 x5 x6; x7 x8 x9]*[x1 x2 x3; x4 x5 x6; x7 x8 x9]' .== Matrix{Float64}(I, 3, 3))

    JuMP.optimize!(model)
    println("got ", objective_value(model), " at ")
    println(" x1:  ", value(x1))
    println(" x2:  ", value(x2))
    println(" x3:  ", value(x3))
    println(" x4:  ", value(x4))
    println(" x5:  ", value(x5))
    println(" x6:  ", value(x6))
    println(" x7:  ", value(x7))
    println(" x8:  ", value(x8))
    println(" x9:  ", value(x9))
end

got 1.5848999999999998 at
x1: 0.7
x2: 0.7
x3: 0.07
x4: -0.4
x5: 0.5
x6: -0.7
x7: -0.5
x8: 0.5
x9: 0.7

Ipopt版本：

using JuMP
using Ipopt
using LinearAlgebra
ask()
function ask()
    lb = [-1, -1, -1, -1, -1, -1, -1, -1, -1]
    ub = [ 1,  1,  1,  1,  1,  1,  1,  1,  1]
    x0 = [0.7, 0.7, 0.07, -0.4, 0.5, -0.7, -0.5, 0.5, 0.7]

    model = Model(Ipopt.Optimizer)
    set_optimizer_attribute(model, "max_cpu_time", 60.0)
    set_optimizer_attribute(model, "print_level", 0)
    set_silent(model)
    
    @variable(model, lb[1] ≤ x1 ≤ ub[1], start = x0[1])
    @variable(model, lb[2] ≤ x2 ≤ ub[2], start = x0[2])
    @variable(model, lb[3] ≤ x3 ≤ ub[3], start = x0[3])
    @variable(model, lb[4] ≤ x4 ≤ ub[4], start = x0[4])
    @variable(model, lb[5] ≤ x5 ≤ ub[5], start = x0[5])
    @variable(model, lb[6] ≤ x6 ≤ ub[6], start = x0[6])
    @variable(model, lb[7] ≤ x7 ≤ ub[7], start = x0[7])
    @variable(model, lb[8] ≤ x8 ≤ ub[8], start = x0[8])
    @variable(model, lb[9] ≤ x9 ≤ ub[9], start = x0[9])

    @NLobjective(model, Min, x1^2+x2+x3^2+x4+x5^2+x6+x7^2+x8+x9^2)
    @constraint(model, [x1 x2 x3; x4 x5 x6; x7 x8 x9]*[x1 x2 x3; x4 x5 x6; x7 x8 x9]' .== Matrix{Float64}(I, 3, 3))

    JuMP.optimize!(model)
    println("got ", objective_value(model), " at ")
    println(" x1:  ", value(x1))
    println(" x2:  ", value(x2))
    println(" x3:  ", value(x3))
    println(" x4:  ", value(x4))
    println(" x5:  ", value(x5))
    println(" x6:  ", value(x6))
    println(" x7:  ", value(x7))
    println(" x8:  ", value(x8))
    println(" x9:  ", value(x9))
end

got -1.8284271244830348 at
x1: -0.500000014712519
x2: -0.7071067831367339
x3: 0.49999998301859216
x4: -0.7071067591675974
x5: 5.788661909852154e-13
x6: -0.707106803904326
x7: 0.5000000173810248
x8: -0.7071067792414213
x9: -0.49999998585490696

2

是不是应该用 @NLconstraint

3

直接改@NLconstraint会报错，不过即使把这句拆解开换成下面九个@NLconstraint约束结果也一样，理解不了哪里错了。。。

@NLconstraint(model, x1^2 + x2^2 + x3^2 == 1.0)
@NLconstraint(model, x1 * x4 + x2 * x5 + x3 * x6 == 0.0)
@NLconstraint(model, x1 * x7 + x2 * x8 + x3 * x9 == 0.0)
@NLconstraint(model, x4 * x1 + x5 * x2 + x6 * x3 == 0.0)
@NLconstraint(model, x4^2 + x5^2 + x6^2 == 1.0)
@NLconstraint(model, x4 * x7 + x5 * x8 + x6 * x9 == 0.0)
@NLconstraint(model, x7 * x1 + x8 * x2 + x9 * x3 == 0.0)
@NLconstraint(model, x7 * x4 + x8 * x5 + x9 * x6 == 0.0)
@NLconstraint(model, x7^2 + x8^2 + x9^2 == 1.0)

发现个问题，这九条约束里3个三参数的单独或一起加的话都没问题，后面6个六参数的任意加一个就跑不动了。Ipopt里九个约束都没问题。

@NLconstraint(model, x1^2 + x2^2 + x3^2 == 1.0)
@NLconstraint(model, x4^2 + x5^2 + x6^2 == 1.0)
@NLconstraint(model, x7^2 + x8^2 + x9^2 == 1.0)

@NLconstraint(model, x1 * x4 + x2 * x5 + x3 * x6 == 0.0)
@NLconstraint(model, x1 * x7 + x2 * x8 + x3 * x9 == 0.0)
@NLconstraint(model, x4 * x1 + x5 * x2 + x6 * x3 == 0.0)
@NLconstraint(model, x4 * x7 + x5 * x8 + x6 * x9 == 0.0)
@NLconstraint(model, x7 * x1 + x8 * x2 + x9 * x3 == 0.0)
@NLconstraint(model, x7 * x4 + x8 * x5 + x9 * x6 == 0.0)