Initially I modeled my objective function as $$\arg \min \operatorname{Var}(f(x),g(x)) + \operatorname{Var}(c(x),d(x)) + \cdots$$where $f$, $g$, $c$, $x$ are linear functions.To be able to solve the problem with linear solvers I have change the problem as follows ($\operatorname{abs}$ stands for absolute value):$$\arg \min\; \operatorname{abs}(f(x)-g(x)) + \operatorname{abs}(c(x)-d(x)) + \cdots$$Is this form correct and has the same meaning as the first model?
Can Variance be replaced by absolute value in this optimization problem
optimization;linear programming;quadratic programming