Is there any Boosting algorithm with closed-form solutions? My goal is to formulate the learning and generalization phases of any Boosting algorithm as a matrix-vector operation.

Through Google, I found a good pdf (*) describing several boosting algorithms but the author Marco Cusumano-Towner only hints and doesn't explain how to recast the boosting algorithms (GradientBoost, Adaboost, QuadBoost) using matrix operations.

My question is:

Can I formulate a boosting algorithm as a regression, a game or a linear programming and arrive at closed-form solution which uses only matrix operations?

(*) Boosting with log-loss
Basically: no.  Boosting is a "meta-method".  If you have a weak learner (an algorithm for learning), it is a way of taking advantage of that weak learner algorithm iteratively to do better at learning some concept than the weak learner would do on its own.

Many/most weak learners don't have a closed-form solution for the model they build; instead, their learning algorithm may fundamentally rely upon iterative methods, optimization algorithms, or other techniques.  As a result, boosting with such a weak learner won't have a closed-form solution, either.