mathematical-optimization - Gurobi：优化二次非 PSD

Question

Gurobi 会优化目标函数不是正定的二次问题吗？我们的约束是线性的——事实上，它们是盒子约束。这是一个已知的 NP 完全问题，根据 Vavasis，非线性复杂性：优化问题，牛津大学出版社。

我们知道 Gurobi 不会优化具有二次约束的二次规划问题，除非在特殊条件下。但是，我们还没有看到它可以或不能处理二次目标函数的具体声明。

Answer 1

Gurobi is designed to handle problems with objective functions that are linear or

• convex quadratic functions for minimization problems
• concave quadratic functions for maximization problems

In addition, it can handle quadratic constraints where the feasible region is convex or a second order cone

You haven't mentioned the type of problem that you are tackling, but if you want to use Gurobi to solve it, the best approach is probably to use its mixed-integer linear optimizer, or use a decomposition method.