Optimization Problem

1

Can we solve the problem \min_{t_1, t_2} \lambda_max(G+t_1H_1+t_2H_2), where G, H_1, H_2, are Hermitian matrices where G not equals any of H_1 or H_1, by using CVX software? (Note: \lambda_max denotes the largest eigenvalue and t_1, t_2 belongs to real numbers.)

2

Are G, H_1, and H_2 inputs to the problem, i…e, known numerical matrices? If so, you ought to be able to enter the problem in CVX almost exactly as written.

lambda_max

maximum eigenvalue of a real symmetric or complex Hermitian matrix. Inside CVX, imposes constraint that its argument is symmetric (if real) or Hermitian (if complex). Convex.

  Disciplined convex programming information:
      lambda_max is convex and nonmonotonic (at least with respect to
      elementwise comparison), so its argument must be affine.
3

Thanks for yours response. Yes, the matrices G, H_1 and H_2 are numerically given.