Xjyuk

The Description of Mithral Armor describes this effect:

Most mithral armors are one category lighter than normal for purposes of movement and other limitations. Heavy armors are treated as medium, and medium armors are treated as light, but light armors are still treated as light.- SRD

The Heavy Armor Optimization feat says:

When you are wearing heavy armor, lessen the armor check penalty of the armor by 1 and increase the armor bonus by 1

There are also feats with identical wording for Medium and Light Armor.

SO

If my intention is to wear Mithral heavy armor would I take the Heavy Armor Optimization or Medium Armor Optimization?

Heavy armor optimization.

It's still heavy armor. It's just treated as medium for movement and other limitations. "Which feats apply" is not a matter of movement or other limitations.

The Dragon #355 Sage Advice column “Official Answers to Your Questions” includes this exchange:

Would the Heavy Armor Optimization feats… apply to heavy armors made of mithral?

No.

Mithral heavy armor effectively becomes medium armor for all purposes, which means that benefits accruing to the wearer of the heavy armor wouldn’t apply when wearing mithral heavy armor. (79–80)

(The sage at the time is Andy Collins.) Thus, according to the sage, if you're wearing mithral heavy armor then you'd need to take the feat Medium Armor Optimization.

Except that there is no feat Medium Armor Optimization.

However, what authority you ascribe to the sage is up to you. Since the feat Heavy Armor Optimization (Races of Stone 41) is itself less than optimal, this DM would be cool with ignoring the sage's advice and letting the benefit of the feat Heavy Armor Optimization apply to mithral full plate or whatever.

Mithral specifically applies to changing limitations of heavy armor. However, the feat in question does not apply to limitations, but the type of armor. This dm would rule that mithral full plate, while treated as medium armor for movement, penalties, class abilities, etc (since those are all "limiting" classifications), would still fulfill the requirements for heavy armor proficiency since heavy armor does not provide a limitation in this case.