Pablo Parrilo has discovered a new approach to convex optimization
that creates order out of chaos in complex nonlinear systems.
ImaGINe YoU aRe hiking in a com- plex and rugged environment. You are surrounded by hills and valleys, mountains, shallow ditches, steep cliffs, and lakes.
Nothing about the ground immediately
around you, or your current direction,
tells you much about where you will end
up or what might lie in between.
Now imagine you are walking on
the inside surface of a huge, smoothly
shaped bowl. You can see the bottom of
it, and even a few steps over the surface
of the bowl tell you much about its shape
and dimensions. There are no surprises.
PHO TOGRAPH B Y PATRICK GILLOOLY
Pablo Parrilo, a professor of electrical engineering and computer science
at Massachusetts Institute of Technology (MIT), has found a way to remake
the mathematical landscapes of complex, nonlinear systems into predictable
smooth bowls. He has constructed a rare
bridge between theoretical math and
engineering that extends the frontiers of
such diverse disciplines as chip design,
robotics, biology, and economics.
Nonlinear dynamical systems are
inherently difficult, especially when
they involve many variables. Often they
act in a linear fashion over some small
region, then change radically in some
other region. Water expands linearly as
new algorithms devised by Pablo Parrilo, an mit professor of electrical engineering and computer science, have made working with nonlinear systems both easier and more efficient.
it warms, then explodes in volume at the
boiling point. An airplane rises smoothly and ever more steeply—until it stalls.
Understanding these systems often requires a great deal of prior knowledge,
plus a painstaking combination of trial
and error and modeling. Sometimes the
models themselves are so complex their
behavior can’t be predicted or guaranteed, and running realistic models can
be computationally intractable.
Parrilo developed algorithms that
take the complex, nonlinear polynomials in models that describe these
systems and—without actually solving
them—rewrites them as much simpler
mathematical expressions represented
as sums of squares of other functions.
Because squares can only be positive, his
expressions are guaranteed to be greater
than zero—the bottom of a “bowl”—
and relatively straightforward to analyze