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At the time of his first lecture in Spring 2009, that number of people had risen to 1000 by his estimation.
Perhaps because the lecture was not videotaped, Boyd revealed more about his professional experiences than he may have otherwise. Boyd would provide optimal solution to the problem, but then that colleague would reply by pointing out its weaknesses. Inevitably, Boyd would respond by reminding that colleague: there was no previous mention of such a constraint.
The new constraint would be accounted for, the problem solved again, and then another round of the same would ensue. Boyd ended the lecture with the moral of his recounting (which I paraphrase): If constraints are incomplete, then an optimal solution cannot be right.
Stephen Boyd did not invent Convex Optimization, but he probably deserves much of the credit for its popularization in engineering. A proof represents culmination of labor that can span many years; indeed, Fermat's last theorem took more than 300 years.


Physicist Richard Feynman calls trivial any proven theorem, but not to diminish the result. So we may interpret disbelief in Convex Optimization as disbelief in the proofs; not disproof, just plain disbelief. What is disquieting about Boyd's revelation is that these particular colleagues are intelligent, successful, and learned people from academia and industry. It was in the middle of the 1980s, when the seminal paper by Kar- markar opened a new epoch in nonlinear optimization. The importance of this paper, containing a new polynomial-time algorithm for linear op- timization problems, was not only in its complexity bound. At that time, the most surprising feature of this algorithm was that the theoretical pre- diction of its high efficiency was supported by excellent computational results. This unusual fact dramatically changed the style and direc- tions of the research in nonlinear optimization.
Thereafter it became more and more common that the new methods were provided with a complexity analysis, which was considered a better justification of their efficiency than computational experiments.


In a new rapidly develop- ing field, which got the name "polynomial-time interior-point methods", such a justification was obligatory.
Afteralmost fifteen years of intensive research, the main results of this development started to appear in monographs [12, 14, 16, 17, 18, 19].
Approximately at that time the author was asked to prepare a new course on nonlinear optimization for graduate students. At the time only the theory of interior-point methods for linear optimization was polished enough to be explained to students. The general theory of self-concordant functions had appeared in print only once in the form of research monograph [12].



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