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The cost function to be minimized by the Simplex algorithm is normally defined as $min(x) = F(x)$ subject to linear constraints $Ax \le b$. Can the cost function be a function of two variables $F(x,u)$ which is subject to constraints $Ax \le B$. As the cost function is dependant on the state of the system?

mlc
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Programmer1
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Yes absolutely, as long as $F(x,u)$ remains linear.

And for the simplex to work, typically variables have to be non negative, so if $u \in \mathbb{R}$ you might need to use the substitution $u:=v-w$ with $v,w \ge 0$.

Kuifje
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  • Thanks for your reply. If I need to find the optimal u(k) that minimises x(k), what kind of cost function can be used to do so? because F(x,u) will give the minimisation of both 'x' and 'u' right? – Programmer1 Mar 05 '17 at 22:40