Objective function Convex proof

Question

This is a question from the textbook that I can trying to figure out.

Show that the objective function $$z = c^{T}x $$ of a linear programming problem is a convex function

I know that $$z = c_{1}x_{1} + .... + c_{n}x_{n}$$ is definition of objective function.

And function f is convex for all $$x, y \in R^{n}$$ $$\lambda \in [0,1]$$ we have $$f (\lambda x + (1 - \lambda)y) \leq \lambda f( x) + (1 - \lambda) f(y) $$

So how do I start this proof...

By $=>$ do you mean greater than or equal to ($\geq$)? If so, don't you have the definition of convex backwards? — Brian Tung, Oct 09 '15 at 00:10

score 0 · Answer 1 · answered Oct 09 '15 at 13:56

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Show that the objective function is linear (a stronger condition than convexity). Can you see how convexity follows?

answered Oct 09 '15 at 13:56

R R

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Could you please name the theorem/lemma that if a function is linear then it's a convex function? – Nick Oct 26 '16 at 04:40

Objective function Convex proof

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