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<body class='hmmessage'><div dir='ltr'>Hi,<br><br>I finally got time to start implementing the alternative method for computing the Hessian of<br>the Lagrangian to do some benchmarking. However, I have come across the following difficulty:<br><br>Using also the Lagrange multipliers as variables yields an Hessian of the Lagrangian in the<br>form of a block matrix: <br><br>H = / H_{xx} H_{xl} \<br> \ H_{xl} 0 /<br><br>Here H_{xx} is the Hessian wrt to the original variables x\inR^n that we are interested in. After calling<br>sparse_hess(tag,n,repeat,x,&nnz,&rind,&cind,&values,&options) I thought that it should be<br>straightforward to identify the parts of rind, cind and values pertaining to H_{xx}. For instance,<br>say we want to count the non-zeros in the first row of H_{xx}, nnz_xx, using the following code:<br><br>int k = 0<br>int nnz_xx = 0<br>while rind[k]==0<br> if cind[k]<n<br> nnz_xx++;<br> end<br> k++;<br>end<br><br>This of course only works provided the non-zeros of H_{xl} are found in the columns>n, but that<br>appears not to be the case.<br><br>Am I missing something really simple here, or how can I extract H_{xx}?.<br><br>Kind regards<br>Ingrid<br><br><br><br><br><div><div id="SkyDrivePlaceholder"></div><hr id="stopSpelling">From: ingridhallen@hotmail.com<br>To: awalther@math.uni-paderborn.de<br>Date: Thu, 11 Apr 2013 09:26:23 +0200<br>CC: adol-c@list.coin-or.org<br>Subject: Re: [ADOL-C] Evaluating Hessian of Lagrangian<br><br>
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<div dir="ltr">Thanks for your reply!<br><br>I think I will do some benchmarking then, to see which<br>of the two approaches works best for my problem.<br><br>The approach suggested by Norm is certainly interesting,<br>but I think I have to little experience with optimization<br>to implement it successfully. At least for the moment.<br><br>Sincerely,<br><br>Ingrid<br><br><br><div><div id="ecxSkyDrivePlaceholder"></div>> Date: Wed, 10 Apr 2013 22:51:22 +0200<br>> From: awalther@math.uni-paderborn.de<br>> To: ingridhallen@hotmail.com<br>> CC: normvcr@telus.net; adol-c@list.coin-or.org<br>> Subject: Re: [ADOL-C] Evaluating Hessian of Lagrangian<br>> <br>> Hi<br>> <br>> sorry for entering the discussion so late but I was on travel<br>> the last days and most of the time offline.<br>> <br>> If you can exploit the minor size of the reduced Hessian<br>> the approach proposed by Norm is certainly the best way to go<br>> since it requires the least number of Hessian vector product<br>> which determines the cost of the derivative calculation.<br>> <br>> However, I am not sure whether Ipopt can really exploit this.<br>> Regarding the other approaches discussed so far:<br>> <br>> We made the experience that it really depends on the application<br>> whether<br>> <br>> * tracing the Lagrangian once with x and lambda as inputs<br>> and evaluating only a part of the Hessian reusing the trace<br>> in all iterations<br>> <br>> or<br>> <br>> * retracing the Lagrangian with x as adoubles and lambda as doubles<br>> in each iteration and computing then the whole Hessian<br>> <br>> performs better in terms of runtime. You could give both approaches<br>> a try and see what works better for you. Both approaches have their<br>> pros and cons with respect to efficiency.<br>> <br>> Best regards<br>> <br>> Andrea<br>> <br>> -- <br>> Prof. Dr. Andrea Walther<br>> Lehrstuhl fuer Mathematik und ihre Anwendungen<br>> Institut fuer Mathematik<br>> Universitaet Paderborn<br>> Warburger Str. 100<br>> 33098 Paderborn<br>> <br>> Email: andrea.walther@uni-paderborn.de<br>> Phone: ++49 5251 602721<br>> ++49 5251 602724 (sekr.)<br>> Fax: ++49 5251 603728<br>> <br>> **********<br>> <br>> <br>> <br></div> </div>
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