I am studying the geometric interpretation of sequential linear programming method.
We consider the one variable problem which is illustrated in the book Engineering Optimization Theory and Practice by Singiresu S. Rao:
Minimize $$f(x) = c_1 x$$ subject to $$g(x) \le 0,$$ where $c_1$ is a constant and $g(x)$ is a non linear function of $x$.
The problem is with the following picture :
I dont understand on what plane they are plotting the curves. How the curve which looks like parabola can represented by the equation $g(x)=0$. I thought that $g(x)=0$ may not look like a continous non linear curve. How $g(x)<0$ is the region above parabola and $g(x)>0$ is below? Please someone help.