Claudia Sagastizábal

Brief Bio

Claudia Sagastizábal is an applied mathematician specialized in optimization with interests in both its theory and its numerical aspects.

After finishing her undergraduate math studies in Argentina, Claudia moved to Paris where she obtained PhD and habilitation degrees at Paris I Panthéon-Sorbonne University. Personal reasons caused Claudia to reverse direction over the Atlantic Ocean about 15 years ago; she now lives in Rio de Janeiro.

Claudia has participated in industrial collaborations since the time of her PhD studies in the 1990s. Her first experience in this area, with Electricité de France (EdF), was so beneficial that it greatly influenced her career: Claudia's theoretical research has been continuously enriched with insight provided by applications.

After graduating, Claudia became a permanent researcher at INRIA, the French Institute for Automatic Control and Computer Science. In Brazil, she had a research position at Eletrobras' Electric Energy Research Center for five years. She has taught optimization at various universities and "Grandes Écoles" and advised many PhD students and post-doctoral fellows in France and Brazil. In parallel with her academic activities, Claudia holds or has held consulting R&D appointments for companies such as EdF, Gaz de France-Suez and Renault in France; Robert Bosch in Germany; and Petrobras, Bovespa and Eletrobras in Brazil.

Claudia participates in numerous synergistic activities. She was elected Council Member- at-large for the Mathematical Optimization Society for the period 2009-2013. She also served on program committees and/or organized thematic clusters on Convex, Nonsmooth and Energy Optimization at the most important conferences in the optimization area. She is an Associate Editor of the journal Energy Systems, has recently ended a five year term as an Editor of Mathematical Methods of Operations Research and will become Editor-in-Chief of the journal Set-Valued and Variational Analysis in 2015.

Claudia is co-author of the book "Numerical Optimization: Theoretical and Practical Aspects," published by Springer. Her research interests lie in the areas of nonsmooth opti- mization, stochastic programming and variational analysis and are driven by real-life applications.

Current Research Field

My research is devoted to Mathematical Optimization, in a broad sense that ranges from theoretical Variational Analysis to algorithms and numerical methods. A vast majority of my works, even the most theoretical ones, hinge upon applications.

In Mathematics, the word "application" refers to a model representing some real-life phenomenon whose behavior we want to understand or to predict, or whose operation we want to improve or control. Optimization has been described as the mathematics of the "betterment": when applied to a real-life problem, Optimization deals with deciding values for model parameters to make some kind of improvement in the real-life situation being modeled.

Consider, for example, the problem of managing a mix of power plants generating electricity. An optimizer can build a model that will guide the plant manager in planning how
much electricity to produce from each source of energy: hydraulic, nuclear, coal, wind, so-
lar. In doing so, the optimization modeler will first define a goal, such as to "minimize the
generation cost", or "maximize the revenue", or "minimize the risk of having a deficit of energy"; this involves optimization of a so-called *objective function*. Naturally, the manager's
choices are limited by the production capacity and physical laws for each technology; these
are examples requiring denitions of *constraint functions*.

Another important request is that demand needs to be satisfied: every time we enter a dark room and switch on the light, we expect electricity to be "waiting" there and the room to be lit. This extremely crucial constraint is difficult to deal with, not only because at planning time the exact amount of (future) demand is unknown, but also because electricity cannot be stored (except for limited amounts in batteries).

Such features can force the modeler to cast the problem in a *stochastic* framework by
incorporating the fact that demand is uncertain.

Once the optimization model is written down, the problem must be solved and here arises
an important consideration. For our example, the manager's decisions have an impact on
the *price* of electricity. From the Optimization point of view, such a value is given by a
"shadow price", the multiplier associated with the demand constraint.

For the manager, in particular, and society, in general, it is therefore very important to compute those prices with high precision.

... but demand is uncertain! What can be done in this situation?

A partial solution is to incorporate in the model as many *scenarios* of demand as possible,
to somehow cover all future outcomes. This makes the optimization problem extremely large,
and special solution methods need to be employed.

By combining Lagrangian relaxation and dualization, our power plant model can be reformulated as a nonsmooth optimization problem. In this context, so-called bundle methods are well-known for their robustness and precision. These nonsmooth optimization algorithms can handle very efficiently large-scale stochastic programming problems such as the one described above. My research focuses on how to exploit structural properties of nonsmooth objective functions arising in this setting, doing so in a manner that accelerates the convergence speed of bundle methods, without losing accuracy in the solution.

Personal Homepage : http://w3.impa.br/~sagastiz/