Dear All,

I am trying to model the following convex constraint in `JuMP`

:

\sum_{i=1}^{k} \lambda_i(X) \geq c,

where X \in \mathbf{S}^n (a symmetric matrix), c is a constant, and \lambda_1(X) \leq \lambda_2(X) \leq \ldots \leq \lambda_n(X) for solving an optimization problem with X as the decision variable. The constraint represents that the sum of k smallest eigenvalues of the symmetric matrix X is greater than c.

Note that the constraint \sum_{i=1}^{k} \lambda_i(X) \geq c is a convex constraint, as the function \sum_{i=1}^{k} \lambda_i(X) is concave on X\in \mathbf{S}^n due to the Raleigh-Ritz formula (also, see the cvxpy link, where it is listed as a concave function).

Is there a way to model such a constraint in `JuMP`

?

Any tips will be much appreciated!