Solving linear optimization problem

Optimization problem is given http://oi49.tinypic.com/xkogmd.jpg>

a(i),b(i) ∈ N, C are given. y(j) – integer variables vector. x(i,j) – binary variables matrix.

What’s the class of this task? MINLP?

As I understand, this function is multi-objective and non-convex so there are no ways to solve it with polynomial time algorithm. Possible variants are only exhaustive search (with some branch and bound optimization) or heuristic methods like genetic algorithm, etc.

Is it possible to solve it using MATLAB or some toolbox?

[Matt J]

Your link didn't work (for me).

[SAUMYA CHATURVEDI]

Hi gratix,

Can you please tell me how to solve the convex optimization problem using polynomial time algorithm in matlab?

Answer 1

[Matt J]

The GA command has mixed integer programming options.