Delivery of Numerical Optimisation exam homework. Claudio Savelli and Bruno Spaccavento
The homework aims to test two different methods for unconstrained nonlinear optimisation problems and compare them. In particular, the two methods taken as reference are the steepest descent and the nonlinear conjugate gradient method with Polak-Ribière. The initial part of the paper will describe the problem and all the mathematical tools required to reach the solutions and, from the data associated with them, analyse the two selected methods. These will be tested on a total of four different functions, which will then be described in detail.
Abstract—The selected problem is the Projected Gradient Method. The objective of this paper is to implement the projected gradient method and then test its effectiveness on a selected problem. The initial part of the paper will describe the problem and all the mathematical tools required to reach the solution. In the second part, the results obtained comparing two methods that will be used to evaluate the gradient, the one with exact derivatives and the one approximated with finite differences, will be analysed.