# Minimization with respect to functional constraints [closed]

I am trying to do the following on Mathematica: Given a pair $(x,y)$, minimize an objective function $f(x,z)$ such that z satisfies $g(x,z) \leq g(x,y)$.

I have defined both functions

f[x_, y_] := ...

g[x_, y_] := ...


Tried the following but it did not work:

x = a number;
y = another number

Min[{f[x, z], g[x, z] <= g[x, y]}, {z, 1, 10}]


Could you help me on that please?

## closed as unclear what you're asking by Daniel Lichtblau, Rahul, m_goldberg, Jens, J. M. is away♦Nov 22 '15 at 3:18

Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

• 1. The minimization functions are FindMinimum[] and NMinimize[]; none of those are in what you've written. 2. You should include the actual functions if you want people to be more helpful. – J. M. is away Nov 21 '15 at 19:46
• Ups I've done a mistake, thanks! I will prepare my question better and ask again. – Nonlinear Nov 21 '15 at 20:04

FindMinimum[{f[x, z], g[x, z] <= g[x, y]}, z][[1]]