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I am trying to solve the following non-convex optimization problem. I'd appreciate any tips or directions.

$ \text{minimize } ||C_1||_2^2 + ||C_2||_2^2$

$ \text{subject to } ||H(C_1 -C_2)||_2^2 \geq 1$

where $||.||_2$ is the $l2$ norm, $C_1$ and $C_2$ are vectors of length $L$ and $H$ is a diagonal matrix.

Lorago
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dsp_guy2020
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  • I think $\text{subject to } ||H(C_1 -C_2)||_2^2 \geq 1$ can be converted w.l.g to $\text{subject to } ||H(C_1 -C_2)||_2^2 = 1$ and then the problem becomes convex with Lagrange multipliers for the constraint. – user619894 May 22 '22 at 07:20
  • The equality constraint has to be affine. – dsp_guy2020 May 24 '22 at 18:53
  • Sorry, don't follow. What is affine constraint and why does the equality need to be one? – user619894 May 24 '22 at 19:02

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