Solve this minimization problem

Hi!

Could you please help me with the following minimization problem. First, we have:

If there would be no t on the right hand side of condition 3, then the problem could be solved by using linprog. Could you please tell me which function I have to use for this problem?

Thank you very much for your time and consideration!

Alex

Answer 1

[John D'Errico]

Nothing you have shown makes this a nonlinear problem. t is a unknown, as is the lambda vector. The only term with t in it has it multiplied by C^, a known constant.

The last time I checked (ok, it was algebra 0, so about 45 years ago), you can simply move the t term to the left hand side of that inequality.

Use linprog. WTP?

[Aleksandrs]

OK. Let's say I want to use linprog. Then without the third condition I would write:

f=zeros(h+1,1)
f(1)=f(1)+1

A=horzcat(zeros(3,1),vertcat(-q1,-q2,ones(1,h)))
b=[-q1hat,-q2hat,1]

linprog(f,A,b,,,zeros(h+1,1))

How should I change my code to include te third condition? Thanks.

[Aleksandrs]

Problem solved.