支持百万级变量的Python大规模凸优化库咨询（CVXOPT溢出）

优化问题形式 #

待求解的凸优化问题完整形式为：

• 目标函数：min p^T*q + |c|
• 决策变量边界约束：
  • lower_bound < q < upper_bound
  • lower_bound < c < upper_bound
• 等式约束：A*q + B*c = b
• 线性边界约束：lower_bound < Rq < upper_bound

当前实现与问题 #

目前基于cvxopt.modeling的核心建模代码如下：

from cvxopt.modeling import variable, op, sum
q = variable(numb_prod, 'q')
c = variable(numb_capacity, 'c')
prod_price = p.trans() * q
problem = op(sum(prod_price) + 1e-6*sum(abs(c)), [constraints])
problem.solve(format='sparse', solver='glpk', options={'glpk':{'msg_lev':'GLP_MSG_OFF'}})

参数说明：p、b为向量，A、B、R为稀疏矩阵，q、c为决策变量。

当前构建的优化问题共包含108575个变量，已超出cvxopt框架的处理能力。经排查，报错并非底层求解器导致，而是cvxopt框架内部实现触发的溢出错误，完整报错栈如下：

Traceback (most recent call last):
File "C:\Users\OsRas\AppData\Local\Continuum\anaconda3\lib\site-packages\IPython\core\interactiveshell.py", line 3325, in run_code
exec(code_obj, self.user_global_ns, self.user_ns)
File "", line 489, in 
q, c, total_cost_x, water_values, list_numb_of_capacity_variables = solution(demand, price_purchase_power, supply)
File "", line 391, in solution
test = problem.solve(format='sparse', solver='glpk', options={'glpk':{'msg_lev':'GLP_MSG_OFF'}})
File "C:\Users\OsRas\AppData\Local\Continuum\anaconda3\lib\site-packages\cvxopt\modeling.py", line 2600, in solve
t = self._inmatrixform(format)
File "C:\Users\OsRas\AppData\Local\Continuum\anaconda3\lib\site-packages\cvxopt\modeling.py", line 2479, in _inmatrixform
for v in variables: vmap[v] = x[vslc[v]]
File "C:\Users\OsRas\AppData\Local\Continuum\anaconda3\lib\site-packages\cvxopt\modeling.py", line 240, in __getitem__
return (+self).__getitem__(key)
File "C:\Users\OsRas\AppData\Local\Continuum\anaconda3\lib\site-packages\cvxopt\modeling.py", line 931, in __getitem__
f._linear = self._linear[l]
File "C:\Users\OsRas\AppData\Local\Continuum\anaconda3\lib\site-packages\cvxopt\modeling.py", line 1385, in __getitem__
for v,c in iter(self._coeff.items()):
OverflowError: Python int too large to convert to C long

核心诉求 #

• 寻找可支持百万级变量规模的Python凸优化库，匹配上述问题的求解需求
• 评估是否必须切换至其他开发语言，才能支撑该规模的优化任务运行

内容的提问来源于stack exchange，提问作者Olba12