Looking skyward

A telescope project as a teenager and a lifelong interest in delving deeper into theory have fueled Jorge Nocedal’s career, one that has spanned from fundamental math and software development to commercializing those methods for use in a range of industries.

For his contributions to the field behind his innovations – mathematical optimization – the Northwestern University professor recently received the 2012 George B. Dantzig Prize, awarded by the Mathematical Programming Society and the Society for Industrial and Applied Mathematics for lifetime achievement.

“This is the biggest prize in my field,” Nocedal says. “I would not have done as much without the support” from the Department of Energy throughout most of his career, much of it for basic science.

Nocedal grew up in Mexico City, reading popular science books and magazines and science fiction. As teenagers, he and his younger brother, Fernando, built a telescope from scratch: They bought parts, ground their own mirror and constructed the mount. Then they took the telescope outside the city to avoid light pollution. They examined the moon and Saturn’s rings and explored the Milky Way. “That’s a hobby that lasted for years,” he says. “We kept improving the telescope, while at the same time reading about the expansion of the universe, the fuel cycle in the sun and so on.”

In college he studied physics. Although fascinated by topics such as quantum mechanics, relativity and optics, Nocedal always was frustrated that courses started with basic, introductory information. He wanted a challenge: the opportunity to study complex topics more deeply. He remembers wondering, “When am I going to be an expert?” So he set up a small group that would read and discuss theoretical physics topics in greater depth.

During college at the University of Mexico, an internship at the Astronomy Institute sparked a shift toward applied mathematics. Nocedal took the internship partly to gain access to instruments he and his brother could use to improve their home-built telescope’s optics. But he was hired to program the computer to optimize a new telescope’s lens design. “Suddenly I was exposed to applied math – not only to applied math, but to optimization,” he says. Soon Nocedal was hooked, and he went to Rice University for graduate studies.

One of the biggest changes has been the increased emphasis on uncertainty in computational modeling.

Mathematical optimization provides a computational framework for solving complex problems. An example of a discrete optimization problem might be to figure the placement of circuit components in a computer chip to minimize energy consumption. Nocedal primarily works on continuous optimization, in which variables can change gradually. His main interest is in problems involving thousands or even millions of variables.

The power industry has used continuous, nonlinear optimization techniques for years to produce and schedule processes that generate power and to calculate the optimal use of resources. Practically, that can unfold in a couple of ways. Because electricity is delivered instantaneously, optimization algorithms allow these systems to constantly adapt to accommodate local failures in a line. Underlying algorithms also can help the power industry handle intermediate-term planning. If a forecast predicts hot weather next weekend, for example, power companies can use optimization algorithms to determine how to generate additional power while minimizing costs.

During most of the 1990s, Nocedal also collaborated with large weather prediction centers on algorithms to produce forecasts. These centers convert data about temperature, air currents and moisture into 10-day global weather predictions. The amount of data involved in such calculations is so massive that the work is done at only a few centers, including one in Washington and another in Europe.

Today, people are applying these ideas to study power use in buildings, which in 2010 consumed more than 40 percent of U.S. energy. At Hancock Place, a 60-story tower in Boston, for example, only one side of the building receives direct sunlight at a time.To minimize energy consumption, the heating and cooling system must constantly adjust to account for changing environmental conditions. That’s a difficult problem, Nocedal says, but one for which researchers are developing increasingly sophisticated solutions.

When he was in graduate school in the 1970s, Nocedal figured he’d work on optimization for five years before moving on to other mathematical questions. But the field blossomed, and the models and tools he works on have become more advanced.

One of the biggest changes has been the increased emphasis on uncertainty in computational modeling, he says. “When I was a grad student, nonlinear models were often formulated as if the data were correct, the models were precise.” As the field has evolved, researchers have gained the tools to consider processes that aren’t completely defined or are noisy. So now, large-scale nonlinear predictions also consider the uncertainty in a fundamental way.

Another question is how to design optimization algorithms for large data sets. Although a lot of data are now available, researchers must understand how to use them properly. “In particular, if you have all this weather information, how much of it is relevant if you want to solve an optimization problem in energy use?” Researchers could use less data to make a fast prediction, he says. Or they might need different types of data to boost a prediction’s accuracy.

Over the past five years, Nocedal has focused much of his research on machine learning, a component of managing big data. “Cloud computing is available and therefore we need optimization algorithms that can make use of a large distributed computing environment.”

Data mining and machine learning include three steps: acquiring data and selecting the relevant features; producing a statistical model; and using that model to make predictions. Optimization algorithms enable harnessing the data to train a statistical model.

Nocedal has worked on predictive models for search engines, voice recognition and computer vision applications. In voice recognition, processing a greater number of voices improves predictions. By taking large numbers of samples from Google Voice, for example, humans can analyze individual vocal frames and feed that information into a statistical model. The optimization algorithms provide ways to adjust the statistical model so it accurately predicts the training data. The resulting mathematical code can be programmed into a cell phone or other device to generate fast and, one would hope, accurate predictions.

As another practical use for his research, Nocedal founded a company, Ziena, which provides software called KNITRO to industry clients, many of them in the energy sector. One of Nocedal’s former Ph.D. students, Richard Waltz, runs the company. Founding Ziena also let Nocedal revisit an old collaboration: He brought his brother Fernando, who had become a Silicon Valley entrepreneur, on for a year as a business strategy consultant.

Because mathematical research often is conducted in small groups, Nocedal’s work provides an example of how basic science produced by a small team can have a broad impact. He and his students know that their software is running on dozens of industrial applications, ranging from energy to computer engineering to biology.

It goes to show, Nocedal says, that with enough patience to become a true expert, “all that analysis and all that thought pays off.”