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 v…

This is the same as -sum of the k largest eigenvalues of X for which a reformulation is given in p. 147 of “Lectures on modern convex optimization” of Ben-Tal and Nemirovski. So for the first k eigenvalues of X, you would do using LinearAlgebra, JuMP n = LinearAlgebra.checksquare(X) # Same as size…

Modeling sum of k-smallest eigenvalues of a symmetric matrix in JuMP

Specific Domains Optimization (Mathematical)

Shuvomoy_Das_Gupta June 20, 2021, 7:59pm 3

This is a great solution, thanks so much @blegat !

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Modeling sum of k-smallest eigenvalues of a symmetric matrix in JuMP

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