$$ \newcommand{\rmap}[3]{#1:#2\rightarrow #3} \newcommand{\lmap}[3]{#1:#2\leftarrow #3} \newcommand{\map}[3]{\rmap{#1}{#2}{#3}} \newcommand{\reals}[0]{\mathbb{R}} \newcommand{\xreals}[0]{\mathbb{R}\cup\{\infty\}} \newcommand{\ub}[1]{\rm{ub\ #1}} \newcommand{\lb}[1]{\rm{lb\ #1}} \newcommand{\glb}[1]{\rm{glb\ #1}} \newcommand{\lub}[1]{\rm{lub\ #1}} \newcommand{\ftom}[4]{\glb{ \left\{#2#1 |\, {}^*#2 = #3\ \rm{and}\ #2^* = #4\right\}}} \usepackage{mathrsfs} \newcommand{\alg}[1]{\mathscr{#1}} \newcommand{\complexes}[0]{\mathbb{C}} $$

The Analysis in Numerical Analysis

When I first undertook a serious numerical computation, Peter Lax' advice was that the more analysis you put into your algorithm, the better the results.

I was asked to lead an optimization team, tasked with computing a set of fudge factors to shape recommendations provided to end users. The objective function was not well suited for gradient methods, and so used a more meticulous search algorithm, which had been implemented before I got involved. Multipliers only made sense when they were positive, so the system contained logic for recovering from the error condition, resulting from the attempt to explore negative multipliers.

I changed the multipliers using a coordinate transformation that eliminated the possibility of the previous negative values, implicitly restricting the search to the space of conceivable parameters.

The result of this change was happy in multiple ways. The search time was materially reduced, as much as by half. And the solutions found were significantly better, increasing compliance and also increasing revenue by and additional 7 figures.

I'm Andrew Winkler. I hope you've enjoyed exploring these ideas with me. Thanks for your time. If you've got any questions, send an email to 4af502d7148512d4fee9@cloudmailin.net.

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