det(exp(X)) = exp(tr(X)). Remarkably, the RHS does not involve off-diagonal elements of X.

Often overlooked: the price of some paths may be highly uncertain.

Does this technique allow construction and SC proof of a barrier for Symmetrized Quantum Relative Entropy (SQRE), defined as SQRE(A,B) = QRE(A,B)+QRE(B,A) ? This would hopefully allow use of a single symmetric cone instead of 2 asymmetirc cones?

Very nice. It would be interesting to see how many "unsolved" (Erling's challenge) problems on ask.cvxr.com could now be conic reformulated, and to what extent computer algebra type techniques might help in finding such refomulations, along the lines of ask.cvxr.com/t/ph-d-thesi... .

I note in passing that I read a new paper today which had 2 instances of "we remark in passing". That's a writing style I associated with decades past, such as a paper I coauthored in "Operations Research" in 1983 which I note in passing used "we note in passing" (attributable to my older coauthor)

Now fixed (at least for me).

Yes, water will freeze at 27 degrees Fahrenheit because the freezing point of water is 32 degrees Fahrenheit, so any temperature below that will cause water to freeze; 27 degrees is below 32 degrees.
Key point: Water freezes at 32 degrees Fahrenheit.

Can single precision cut the mustard on first order methods, such as PDHG for LP (perhaps if followed, if needed, by some type of repair step or crossover in double precision)?

Sorry. I meant single vs. double precision.

What precision is used on GPU?

Corollary: If if A and B are symmetric d x d matrices and B is positive definite, then AB is diagonalizable.

How does energy (electricity) used to solve the problem compare between GPU and CPU?

SR1 is a fairly well-known Quasi-Newton update. Most frequently used in conjunction with Trust Regions on indefinite Lagrangians.

SR! Quasi-Newton update is same as SR1, except for holding on to the shift key too long after the R. Most frequently used by older people with declining visual acuity.

A crappy simulation is a crappy simulation, whether or not it's called a Digital Twin.