Hello

I'm trying to solve some problems on Nonlinear Optimization. I have the book "Nonlinear Optimization" - by Andrzej Ruszczyński, 2006.

It's problem 3.8 and sounds as follows.

The output variable of a system depends on the input variable . We have collecred observations , for different settings of the input variable, with .

(a) We know that the dependence of on should be nondecreasing. Formulate the problem of finding new values such that and the sum of the squares of adjustments is minimized.

(b) We know that the dependence of on should be convex and nondecreasing. Formulate the problem of finding new values such that this is satisfied and the sum of the squares of adjustments is minimized.

I'm a bit puzzled of what he means with "the dependence of on should be nondecreasing" and "the dependence of on should be convex and nondecreasing"

In (a) I have formulated the optimization problem as:

and have defined my 's as:

and

.

But as I wrote, I'm a bit lost on what he wants me to do ?

Can anyone enlighten me ?