I'm trying to solve/define the following optimization problem: $\max_M f(M)$ s.t. $M \theta = b$ $\sum_j \theta_j = 1$
When: M is an m*n real matrix $\theta$ and $b$ are n*1 column vectors. f returns a real scalar.
I cannot seem to recall, find a reference, or even define the name of this problem.
What are standard regularity conditions imposed (in terms of $f()$ and $M$) for a solution to exist? What would be the relevant first and second order conditions?