1. ## Optimization problem

Hello,

I have the following question:

max/min $\displaystyle w=f(x_{1},x_{2},...,x_{n})$ subject to $\displaystyle g(x_{1},x_{2},...,x_{n})=0$ and $\displaystyle a_{1} \leq x_{1} \leq b_{1}, a_{2} \leq x_{2} \leq b_{2},...,a_{n} \leq x_{n} \leq b_{n}$

I need the solution of the above question and also I want to guide me the references related to this problem.

2. Originally Posted by raed
max/min $\displaystyle w=f(x_{1},x_{2},...,x_{n})$ subject to $\displaystyle g(x_{1},x_{2},...,x_{n})=0$ and $\displaystyle a_{1} \leq x_{1} \leq b_{1}, a_{2} \leq x_{2} \leq b_{2},...,a_{n} \leq x_{n} \leq b_{n}$

Any hypothesis for $\displaystyle f$ and $\displaystyle g$ ?

3. Originally Posted by FernandoRevilla
Any hypothesis for $\displaystyle f$ and $\displaystyle g$ ?
The only hypothesis is their higher partial derivatives exists with respect to their arguments.

4. Originally Posted by raed
Hello,

I have the following question:

max/min $\displaystyle w=f(x_{1},x_{2},...,x_{n})$ subject to $\displaystyle g(x_{1},x_{2},...,x_{n})=0$ and $\displaystyle a_{1} \leq x_{1} \leq b_{1}, a_{2} \leq x_{2} \leq b_{2},...,a_{n} \leq x_{n} \leq b_{n}$

I need the solution of the above question and also I want to guide me the references related to this problem.
That is virtually the definition for the general constrained optimisation problem, you won't get a solution without being more specific about f and g.

CB