writing a linprog command for this optimisation p

I want to maximise a matrix x, the size of which is 5 × 5, for example. Subject to the following constraints:

. Also, there is another constraint: .

I am confused about how I can represent these constraints as matrices. Each individual represents an element of the matrix x, which is to be maximised? How do I go about this?

[Walter Roberson]

Consider using Problem Based Optimization to describe the system.

[Torsten]

What do you mean by "maximize a matrix" ?

Maybe

sum_{i=1}^{i=5} sum_{j=1}^{j=5} x_ij

?

[John D'Errico]

Maximizing a matrix is meaningless. You need to decide WHAT to maximize about that matrix. What is as large as is possible? Until you define what it is you need to do, there is nothing to do. As far as the constraints are concerned, just unroll the matrix into a vector of 25 elements, effectively using reshape. You have 9 linear inequality constraints that you have described. Each one of them is ONE constraint. You can write each of them as a linear inequality constraint involving 2 of the 25 unknowns in your matrix.