Models that include a hill-climbing component

I’d like to have a model in Stan where the data is drawn from a distribution that is a dependent on the parameters but where the dependency involves hill-climbing on a cost function. If I were coding this “normally”, I’d use simplex or something like that.

I think this is different, but similar, to using algebra_solver_newton, though I could calculate the gradient of my cost function and either use that solver or simply take some steps in the direction of the gradient. Can someone point me in the right direction?

Thank you in advance.

PS I’d call this “optimization”, but searching for that means that I find lots of webpages on using Stan to optimize and thereby find MAP estimates. If I search from “simplex”, I get lots of pages about Dirichlet distributions. Argh.

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Could you please be more specific on what is being represented with simplex?

Sorry. I mean that i would use the simplex algorithm (eg see here: Simplex algorithm - Wikipedia). Make more sense?