线性不等式约束不适用于德雷克

问题描述

我正在学习如何使用 Drake 解决优化问题。 这个问题是为了找到栅栏的最佳长度和宽度，栅栏的周长必须小于或等于 40。下面的代码仅在周长约束是等式约束时才有效。它应该作为一个不等式约束，但我的最佳解决方案导致 x=[nan nan]。有谁知道为什么会这样？

from pydrake.solvers.mathematicalprogram import MathematicalProgram,Solve
import numpy as np
import matplotlib.pyplot as plt

prog = MathematicalProgram()

#add two decision variables
x = prog.NewContinuousVariables(2,"x")

#adds objective function where
#
# min 0.5 xt * Q * x + bt * x
#
# Q = [0,-1
#      -1,0]
#
# bt = [0,#      0]
#
Q = [[0,-1],[-1,0]]
b = [[0],[0]]
prog.AddQuadraticCost(Q,b,vars=[x[0],x[1]])

# Adds the linear constraints.
prog.AddLinearEqualityConstraint(2*x[0] + 2*x[1] == 40)
#prog.AddLinearConstraint(2*x[0] + 2*x[1] <= 40)
prog.AddLinearConstraint(0*x[0] + -1*x[1] <= 0)
prog.AddLinearConstraint(-1*x[0] + 0*x[1] <= 0)

# Solve the program.
result = Solve(prog)
print(f"optimal solution x: {result.GetSolution(x)}")

解决方法

对于不等式约束和等式约束，我得到 [nan,nan]。

正如 Russ 所提到的，问题在于成本是非凸的，而 Drake 导致了错误的求解器。目前，我建议明确指定一个求解器。你可以这样做

from pydrake.solvers.ipopt_solver import IpoptSolver
from pydrake.solvers.mathematicalprogram import MathematicalProgram,Solve
import numpy as np
import matplotlib.pyplot as plt

prog = MathematicalProgram()

#add two decision variables
x = prog.NewContinuousVariables(2,"x")

#adds objective function where
#
# min 0.5 xt * Q * x + bt * x
#
# Q = [0,-1
#      -1,0]
#
# bt = [0,#      0]
#
Q = [[0,-1],[-1,0]]
b = [[0],[0]]
prog.AddQuadraticCost(Q,b,vars=[x[0],x[1]])

# Adds the linear constraints.
prog.AddLinearEqualityConstraint(2*x[0] + 2*x[1] == 40)
#prog.AddLinearConstraint(2*x[0] + 2*x[1] <= 40)
prog.AddLinearConstraint(0*x[0] + -1*x[1] <= 0)
prog.AddLinearConstraint(-1*x[0] + 0*x[1] <= 0)

# Solve the program.
solver = IpoptSolver()
result = solver.Solve(prog)
print(f"optimal solution x: {result.GetSolution(x)}")

我将在 Drake 方面进行修复，以确保当您有非凸二次成本时它会产生正确的求解器。