You plan to perform a portfolio optimization exercise on a set of $10$ stocks

$($a$)$ You plan to set the following constraints: $($a$)$ Full Investment constraint $($b$)$ Position Limit constraint and $($c$)$ Box constraint $($d$)$ Group Constraint and $($e$)$ Return constraint. What would be the impact of each of the constraints on the final output?

$($b$)$ Specify at least three different portfolio objectives that can be set and explain briefly about each of the objectives

$($c$)$ Identify at least four different ways in which a portfolio can be optimized based on the above objectives and constraints.