半定规划中的绝对值约束之和 [英] sum of absolute values constraint in semi definite programming

问题描述

我想对我的世界进行半定规划优化，以绝对值之和为约束.例如:

I want to further my real world semi definite programming optimization problem with a constraint on sum of absolute values. For example:

abs(x1) + abs(x2) + abs(x3) <= 10.

我已经搜索了互联网和文档，但是找不到代表这种情况的方法.我正在使用python和cvxopt模块.

I have searched internet and documentation but could not find a way to represent this. I am using python and cvxopt module.

推荐答案

您的约束等效于以下八个约束:

Your constraint is equivalent to the following eight constraints:

 x1 + x2 + x3 <= 10
 x1 + x2 - x3 <= 10
 x1 - x2 + x3 <= 10
 x1 - x2 - x3 <= 10
-x1 + x2 + x3 <= 10
-x1 + x2 - x3 <= 10
-x1 - x2 + x3 <= 10
-x1 - x2 - x3 <= 10

我没有使用过cvxopt，所以我不知道是否有更简单的方法来处理该程序包的约束.例如，您的约束等效于|x|_1 <= 10，其中|x|_1是x的1范数.

I haven't used cvxopt, so I don't know if there is an easier way to handle your constraint with that package. For example, your constraint is equivalent to |x|_1 <= 10, where |x|_1 is the 1-norm of x.

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