Convex Optimization - last lecture at Stanford

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Last lecture of a decade

I attended Stephen Boyd's class on Convex Optimization in 1999. At that time, there was no book; just Boyd's lecture notes and figures drawn free hand. Boyd said there were about 100 people in the world who understood the topic.

I attended Boyd's class again in 2009. By this time, that number had risen to 1000 in his estimation.

It was fascinating to witness evolution of his Course at Stanford over that ten year period; but more fascinating were the last 10 minutes of this last class.

Perhaps because the lecture was not taped, he revealed more about his professional experiences than he may have otherwise. Certainly, this was something he had not shared throughout the preceding lectures which were quite academic in the best sense...

Revelation

Some of Boyd's colleagues and contemporaries "don't believe" in Convex Optimization.

The beauty of mathematics is that it is either right or it is wrong; e.g., the left side of an equation equals the right side. There is little room for interpretation as there may be in other disciplines; e.g., Law. Mathematical results are traditionally presented within a theorem/proof paradigm. A proof represents culmination of effort that can span many years. Richard Feynman calls "trivial" any proven theorem, but not to diminish the result.

So we may interpret their disbelief in Convex Optimization as a disbelief in the proofs; not a disproof, just disbelief.

Boyd recounted several incidents over his career in a hunorous and entertaining manner.


Background

Stephen Boyd did not invent Convex Optimization, but he probably deserves most of the credit for its recent popularization:

  • Boyd was able to interpret and distill the complicated mathematics of Convex Analysis and then present its essence in a way that is accessible to engineers.
  • Boyd demonstrated applications of Convex Optimization to Control Theory and Circuit Analysis to which he made important contributions.

The consequence of his efforts is to bring an obscure topic mainstream (Convex Optimization is now a mandatory course at Stanford), and he has the most successful and widely read book on the subject (reckoning by Amazon.com) since 2004.

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