the purpose of this exercise is to derive the dual program ( from the primal program ( the starting point is to introduce vector of auxiliary variables :[ xn ]and write the primal program as xi aka , , = min subject tox yi ( {ka} xi ( (aapply the lagrangian optimization theory from section to obtain the lagrangian function ({ ax}{lu})where and are the lagrange multipliers corresponding to the first and second inequality constraintsrespectively (bshow that the karush-kuhn-tucker (see theorem conditions for optimizing are ly / ( lx li (yi (xi xi yi (xi xi ( here stands for componentwise multiplicatione [ yn ln ]and we have abbreviated {ka} to (xi )in view of ( [hintone of the kkt conditions is uthus we can eliminate (cusing the kkt conditions ( )reduce the lagrange dual function ( :mina , , ({ ax}{ }to (ln = li xx li yi (xi = = ( (das consequence of ( and ( )-( )show that the optimal prediction function gt is given by gt (xa yi li (xi )( = where is the solution to max (ll subject toly and ( pn = yi li (xi for any such that ( consider svm classification as illustrated in figure the goal of this exercise is to classify the training points {(xi yi )based on the value of the multipliers {li in exercise let xi be the auxiliary variable in exercise