MATLAB: The best way to write a large number of constraints for an optimization problem

optimization

Hi All,

I have an optimization problem which have a larger number of variables, probably 10000 optimization variables and a large number of constraints. The optimization problem is mixed integer convex problem. What is the best way to define the large number of constraints?. Can I use loops like the ones used in CVX to define constraints?. I have matlab 2013a.

Thank you

Best Answer

If they are linear constraints, they will be expressed using matrix-vector multiplication

A*x<=b
Aeq*x<=beq

so any vectorized method for building the A, Aeq, b, beq, matrices would be appropriate. Similarly, nonlinear constraints in Matlab are expressed using user-defined constraint functions of the following form

function [cineq,ceq]=nonlcon(x)
  ....
end

where cineq and ceq are vectors of inequality and equality constraint violations, respectively. When the number of variables or constraints is large, you would use vectorized Matlab commands to generate cineq and ceq from x.

Related Solutions

MATLAB: Dynamic bounds in an optimizer

You are describing a nonlinear constraint. This is a type of constraint that simulannealbnd cannot handle.

In fact, your constraint is not differentiable. This can be a problem for solvers. However, if your underlying variables are integer-valued, then you can use some techniques from integer linear programming to create the constraint. See Optimal Dispatch of Power Generators for an example.

Solvers that can handle nonlinear constraints include fmincon, patternsearch, ga, and the recent version of surrogateopt. Solvers that handle integer variables include intlinprog, ga, and surrogateopt.

Alan Weiss

MATLAB mathematical toolbox documentation

MATLAB: Optimization Constraints

I think i can use the argument nonlcon in fmincon function.

function [cineq ceq] = nonlcon(x)
ceq sum(abs(x))-1;
cineq = [];
end
fmincon(@myfun,A,b,Aeq,beq,lb,ub,@nonlcon,options);

Anyone can confirm that?

Best Answer

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MATLAB: Dynamic bounds in an optimizer

MATLAB: Optimization Constraints

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