# BEST LAMBDA

Choose the best value for the Tikhonov regularization parameter lambda

## Contents

Function of MOBY-DIC TOOLBOX.

## Description

Consider the following regularized least squares optimization problem:

subject to:

Call H = G'G, Q = L'L, y = G'd. If a test set matrix Gt and a test vector dt are not null, lambda is found in order to minimize . If they are null, is chosen with a generalized cross validation technique (see function GCVcost). This function uses a nested function 'solve' which determines the cost associated to a given value of , by solving the optimization problem. A handle to this function is passed to Matlab function fmincon which finds the value of lambda minimizing the cost.

## Syntax

**lambda = bestLambda(H,Q,y,G,d,Gt,dt,constraints,solver)**

H, Q, y, G are the matrices defining the cost functional. Gt and dt are the matrices used as test set. constraints is a structure with fields A, B, Aeq, Beq representing the constraints matrices. solver is a string specifying the solver you want to use to solve the QP problem (this is necessary only in presence of constraints. Possible choices are 'quadprog' (default), 'cvx', 'cplex', 'yalmip', 'clp'.

## Acknowledgements

Contributors:

- Alberto Oliveri (alberto.oliveri@unige.it)

Copyright is with:

- Copyright (C) 2012 University of Genoa, Italy.