I have encountered this optimization problem
while trying to implement the method proposed in this very interesting paper:
the thing is that the optimization is a constrained nonlineal optimization. So far my colleagues and I have found a great solution using fmincon, a Matlab function which is part of the optimization toolbox. However we need to implement our solution in c++. While working with Matlab we got a warning saying that the software was going to use an active-set method, and here
it says that the way it handles the optimization is by using SQP (sequential quadratic programming), but for that it solves a quadratic subproblem , and I quote : "Here you simplify Equation 2-1 by assuming that bound constraints have been expressed as inequality constraints. You obtain the QP subproblem by linearizing the nonlinear constraints."
My question to this community is: how can I linearize the constraints, knowing that they are expressed in the form of a distance between two points that should be equal to a number that is well known ?(basically the constraint says that the lengths of the bones of a person must not change between different frames while being acquired with the kinect).
Any help in this matter will be greatly appreciated, I just need you to point me to the correct literature on how to solve this kind of optimization problems, since fmincon source code is not very clear.