Wednesday, June 18, 2008

Your career, death valleys, and ... nonlinear programming

On the trail of science and corporate analogies started with "Using magnets to understand the corporate culture", I wanted to explore the similarity between mathematic optimization and corporate culture.

Traditional non-linear algorithms can end up in local minimums, or "death valleys", like the ones highlighted in "white".

In nonlinear programming, the objective is to determine the minimum value for an object function within a set of constraints. Some of the most popular techniques (at least back in the early 90's when I studied them) involved a starting point on the surface of the constrained solution space and, from those coordinates, a slight step towards a new set of variables that resulted in a lower function value.

There is a bit more to it, but when the solution space is convex, you can repeat the series of small steps continuously, achieving ever lowering function values until you reach the variables that result in the minimum value for the function.

A convex space is a solution space where you can connect all points within the space using a direct line that never leaves the space. In simpler terms, the interior of a sphere is a convex space; the interior of a U-shaped pipe is not.

Finding a solution within a non-convex space is quite more difficult because the algorithms that lead to the next set of variables favor immediate decreases in the value of the target function. When applied to a non-convex space, the conventional solutions may lead to a "local optima" point from where there is no escape. In other words, the algorithm "cannot see" a better solution because all the immediate alternatives look worse than the current one. In the illustration, the variables of "Quality" and "Execution" time on a hypothetical "Cost" function have "local optima" points highlighted in white, whereas the global minimum is highlighted in yellow.

What it means to you

This analogy works for an entire company or for a single individual, but think of how many times in life we settle for a "local optima" situation where we feel lost and without direction, with each step pointing to a potentially worse situation.

Think of how many times choosing the best short-term direction can lead you to a comfort zone from where it is difficult to escape. I call those zones "death valleys". Think of it: not leaving a dead-end job because your next evaluation may get hurt or because that long awaited promotion may take an extra couple of years; not taking that class because you can get one more assignment done and improve your chances of a better evaluation.

I know we are not points searching for a point of "local optima" in a 3D chart. The solution spaces are far from convex. Even worse, they are not static and are affected by our presence.

Whereas finding a better "local optima" or the elusive "global optima" in the realm of nonlinear programming requires exhaustive search, in real life it requires curiosity and friends who can tell you about what different parts of the chart look like.

Better solutions require different starting points

Knowing about the work of others gives you access to different starting points from where you can reach a better solution. Whether a "better solution" means a more fulfilling career or an improved work life balance, the choice is yours.

Of course, just knowing about a better solution is not sufficient, as the effort required to get there may not be worth the benefits. As an example, knowing that an SAP consultant makes twice your salary may not be a sufficient motivator to make you divert time from your family to study SAP skills in the wee hours of the night. Once again, the choice is yours.

Having others knowing your work is equally important as your peers can use their own vantage points to tip you into a better solution. Good mentors are great assets there.

A pretty chart (it is pretty, isn't it, took me a while to convince MS-Excel to play along) and some words cannot motivate anyone, but they can plant a seed. Whether you take on an off-chance skunkwork project, take in a couple of mentees, start that hobby, there are always ways to start leaving an uncomfortable situation in work and life.

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