Document what cost function LogisticRegression minimizes for each solver

Description

Different choices of solver for sklearn's LogisticRegression optimize different cost functions - its highly confusing behavior, particularly of concern if you want to publish what cost function you're using. In particular:

sklearn.LR(solver=liblinear) minimizes: L + lam*Rb
sklearn.LR(solver=others) minimizes:    L + lam*R
statsmodels.GLM(bionomial) minimizes:   L/n + lam*Rb

where:

lam = 1/C
L = logloss
n = training sample size
R = square of L2 norm of feature weights
Rb =square of L2 norm of feature weights and intercept

I was a little surprised to find that the logloss is not normalized by the training set size. I think this is uncommon, and means the effective C changes based on the amount of training data. Good thing, bad thing? Not sure, but it seems unusual, but more importantly, what is minimized should be explicit.

PS. https://github.com/scikit-learn/scikit-learn/pull/10001 --- excellent idea! The default liblinear cost function is just plain confusing.

Steps/Code to Reproduce

There's an example to show the different weights here:

https://stackoverflow.com/questions/47338695/why-does-the-choice-of-solver-result-in-different-weight-in-sklearn-logisticreg

Expected Results

Actual Results

Versions

1.19.1

Start with the LogisticRegression documentation and its solver descriptions, then compare the stated objectives for liblinear and the other solvers with the existing text. Done means the minimized cost function, regularization terms, intercept treatment, and normalization are explicitly documented for each solver.