<html>
<head>
<meta http-equiv="Content-Type" content="text/html; charset=us-ascii">
</head>
<body style="word-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;" class="">
Sorry for the time travel. As far as I know, optimization over complex-valued parameters is not a well-defined problem. I am not sure how you can develop an optimization algorithm for it. Perhaps our optimization experts have better suggestions in this direction.
<div class=""><br class="">
</div>
<div class="">The real-valued formulation seems to be more promising to me. The preconditioning is hard, but still doable with fieldsplit as Mark mentioned.</div>
<div class=""><br class="">
</div>
<div class="">Hong (Mr.)<br class="">
<div><br class="">
<blockquote type="cite" class="">
<div class="">On Apr 14, 2020, at 1:42 PM, Sajid Ali <<a href="mailto:sajidsyed2021@u.northwestern.edu" class="">sajidsyed2021@u.northwestern.edu</a>> wrote:</div>
<br class="Apple-interchange-newline">
<div class="">
<div dir="ltr" class="">
<div class="">
<div dir="ltr" class="">
<div class="">Hi Hong, <br class="">
<br class="">
</div>
Apologies for creating unnecessary confusion by continuing the old thread instead of creating a new one.
<br class="">
<br class="">
</div>
<div class="">While I looked into converting the complex PDE formulation to a real valued formulation in the past hoping for better performance, my concern now is with TAO being incompatible with complex scalars. I would've preferred to keep the complex PDE
formulation as is (given that I spent some time tuning it and it works well now) for cost function and gradient evaluation while using TAO for the outer optimization loop.
<br class="">
<br class="">
</div>
<div class="">Using TAO has the obvious benefit of defining a multi objective cost function, parametrized as a fit to a series of measurements and a set of regularizers while not having to explicitly worry about differentiating the regularizer or have to think
about implementing a good optimization scheme. But if it converting the complex formulation to a real formulation would mean a loss of well conditioned forward solve (and increase in solving time itself), I was wondering if it would be better to keep the complex
PDE formulation and write an optimization loop in PETSc while defining the regularizer via a cost integrand.<br class="">
</div>
<br class="">
</div>
Thank You, <br class="">
<div class="">
<div dir="ltr" class="gmail_signature">
<div dir="ltr" class="">
<div class="">
<div dir="ltr" class="">
<div class="">
<div dir="ltr" class="">
<div style="font-size:12.8px" class="">Sajid Ali | PhD Candidate<br class="">
</div>
<div style="font-size:12.8px" class="">Applied Physics<br class="">
</div>
<div style="font-size:12.8px" class="">Northwestern University</div>
<div style="font-size:12.8px" class=""><a href="http://s-sajid-ali.github.io/" target="_blank" class="">s-sajid-ali.github.io</a></div>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
</blockquote>
</div>
<br class="">
</div>
</body>
</html>