How can I solve a nonlinear optimization problem including partial derivatives?

I am working on solving a Black-Scholes-like nonlinear PDE arising from a commodity storage valuation problem. My problem is this: I am to find an optimal control c_optimal by solving a maximization problem somewhat similiar to the example shown on slide 11 here, and afterwards use said c_optimal in solving the PDE. However, the maximization problem includes a V_I term, the first derivate in I direction (storage volume). Is it possible to use the fminsearch MATLAB function in this case? Do you have any better ideas?

[Matt J]

It's not clear why the presence of V_I complicates anything. If it's just a constant independent of the scalar, c, then yes, fminsearch should be able to handle it, as long as a(I,c) has decent continuity in c. fminbnd might be better, since you have those cmin and cmax bounds.