Find optimal values while minimising multiple multi-variable functions

I have 4 multi-variable functions defined as

= ,

= ,

= ,

= .

I am using symbolic expression to represent the functions. I want to compute the optimal values of and (starting value of all is same at ) that minimizes , under some specific constraints such as

• , , , .
• 

I tried using Solve function of matlab to find suitable solution under the parameter and using equations of form , but I am not getting any proper solution.

I hope some of you help my trouble.

[Alan Weiss]

Are you using the problem-based approach using optimization variables? Or are you using Symbolic Math Toolbox™ functions? I recommend Optimization Toolbox™ functions because they are numeric, and hence can reliably find solutions. It is not always possible to find a symbolic solution.

Alan Weiss

MATLAB mathematical toolbox documentation

[Matt J]

@Sumana Bag Your problem statement appears to involve only E1,...,E4. What role do f1,...,f4 have in the problem?

Also, what properties do the E1,...,E4 functions have? Are they linear? smooth? piecewise-smooth?...

[Sumana Bag]

@Alan Weiss I am using symbolic math toolbox to find genereic solutions. Is there any way to construct the above minimization problem using symbolic expressions only?

@Matt J f1,...,f4 doesn't significantly effect the problem formulation. The main minimization problem only invloves E1,...,E4. These E1,...,E4 functions are non-linear functions.