<div dir="ltr"><div dir="ltr"><br></div><div class="gmail_extra"><br><br><div class="gmail_quote">On Thu, Aug 8, 2013 at 3:38 PM, Nicolas Bock <span dir="ltr"><<a href="mailto:nicolasbock@gmail.com" target="_blank">nicolasbock@gmail.com</a>></span> wrote:<br>
<blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div dir="ltr">Hi,<div><br></div><div>Suppose I would like to maximize</div><div><br></div><div>max_{X} [ Tr(C X) ]_{+}</div>
<div><br></div><div>where [z]_{+} = max(z, 0), the hinge loss function.</div></div></blockquote><div><br></div><div><br></div><div>You can simply maximize</div><div> </div><div> max_{X} Tr(CX)</div><div><br></div><div>subject to whatever constraints you have. </div>
<div> </div><div>if the optimal value is negative, then that optimal solution is still optimal for your original objective with the optimal value of Tr(CX)_{+}=0.</div><div> </div><div>If the optimal value is nonnegative, then optimal solution to the Tr(CX) problem is still optimal for the original problem. </div>
<div> </div><div>There's no need to add a slack variable. </div></div></div><br clear="all"><div><br></div>-- <br>Brian Borchers <a href="mailto:borchers@nmt.edu" target="_blank">borchers@nmt.edu</a><br>
Department of Mathematics <a href="http://www.nmt.edu/~borchers/" target="_blank">http://www.nmt.edu/~borchers/</a><br>New Mexico Tech Phone: (575) 322-2592<br>Socorro, NM 87801 FAX: (575) 835-5366
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