optimal control

*To*: mathgroup at smc.vnet.net*Subject*: [mg4839] optimal control*From*: George Melikian <melikian at ups.edu>*Date*: Fri, 20 Sep 1996 01:12:52 -0400*Sender*: owner-wri-mathgroup at wolfram.com

Hello, I am having some difficulty setting up an optimal control problem on Mathematica. The problem is as follows: The control variable (u) denotes a threshold setting (0<u<1) that is placed between 2 probability densities (h & t). The objective is to maxize the payoff (w) while considering changing risks over time (r(t)). Here is the code: v = BetaDistribution[9,3]; r[t_] := PDF[v,t]; h = NormalDistribution[0,.1]; e = NormalDistribution[.3,.1]; g[u_] := CDF[h ,u]; b[u_] := CDF[e ,u]; w[u_,t_] := g[u]+(1-b[u])r[t]- b[u]r[t]- (1-g[u]); te= Simplify[ D[w[u,t],t]]; hamiltonian = w[u,t] + lambda te; The problem comes when I attempt to solve for the partial derivatives of the hamiltonian with respect to: each (u,t,lambda). i.e. D[Hamiltonian, lambda] or Solve[ D[Hamiltonian,lambda]==0, lambda] I get an error telling me either 1/0 encountered or that the function cannot be solved. Any help here would be greatly appreciated. Thanks in advance, George Melikian Melikian at ups.edu ==== [MESSAGE SEPARATOR] ====