How to speed up run time?

7

@Erling When log_det is reformulated for CVXQUAD, CVX sends SOCP to the solver (Mosek), not SDP.

From my write up in CVXQUAD: How to use CVXQUAD's Pade Approximant instead of CVX's unreliable Successive Approximation for GP mode, log, exp, entr, rel_entr, kl_div, log_det, det_rootn, exponential cone. CVXQUAD's Quantum (Matrix) Entropy & Matrix Log related functions

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Replace
log_det(cvx_expression) >= t where cvx_expression is an n by n matrix
with

    variable u     
    -rel_entr(1,u) >= t/n
    det_rootn(cvx_expression) >= u

+++++

Replace
log_det(cvx_expression) , where cvx_expression is an n by n matrix
with
z
and add

    variables u  z % this line must be before u or z are used
    -rel_entr(1,u) >= z/n
    det_rootn(cvx_expression) >= u

+++++

Note: A simpler to write reformulation (NOT RECOMMENDED) can be used:
Replace
log_det(cvx_expression)
with
-quantum_rel_entr(eye(size(cvx_expression)),cvx_expression)

However, as discussed below, use of quantum_rel_entr is computationally demanding. Formulation using quantum_rel_entr consumes much more computational resources than that used by preceding formulations.

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CVXQUAD actually formulates 2 by 2 LMIs for the above (scalar) cases, and these are sent to the solver (Mosek) by CVX as SOCPs. As described in my linked write up, CVXQUAD only sends LMIs (SDPs) to the solver when Quantum (Matrix) Entropy and Matrix Logarithm related functions, such as quantum_rel_entr, are used.