Error bound for a perturbed minimization problem related with the sum of smallest eigenvalues (Q5962400)

For an arbitrary symmetric \(n \times n\) matrix \(C\) and a fixed integer \(1 \leq k \leq n\) the author studies the minimization problem \(m(\epsilon):=\min_X \{ Tr\{ CX \}+\epsilon f(X) \}\) , where \(X\) is an \(n \times n\) symmetric matrix, whose eigenvalues satisfy \(0 \leq \lambda_i(X) \leq 1\) and \(\sum_{i=1}^n \lambda_i(X)=k\), \(\epsilon > 0\) is a perturbation parameter and \(f\) is a Lipschitz-continuous function. He establishes lower and upper bounds for the minimization function \(m(\epsilon)\).