Post date: May 28, 2017 8:27:11 PM
Interior-point method [1] and penalty method [2] are both used to solve nonlinear, constrained optimization of the following general form
The interior-point method replaces the constrained problem with an unconstrained one by using a barrier function, e.g. for a logarithmic barrier function
and then apply gradient descent to solved the latter, i.e. the gradient is given by
The penalty method also makes use of a barrier function, but replaces the constrained problem with a series of unconstrained one whose solutions ideally converge to the solution of the original constrained problem. For example, with a max barrier function
In each iteration
of the method, is increased (e.g. by a factor of 10) to solve the unconstrained problem and the solution is used as the initial guess for the next iteration