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# Optimization and Electrical Energy

## Team and Interlocutors

C. Gonzaga, A. Iusem, J. M. Martinez e seus colaboradores especialmente no IMPA e UNICAMP.

## Research Topics

Optimization is a set of mathematical problems with a broad scope of almost direct applications in Engineering, Physics, Chemistry, Economy, Social Sciences and other branches of human knowledge. On the other hand, Operations Research is the set of problems and methods related to the process of making decisions. Therefore, Operations Research uses intensively techniques from Optimization, but also from Probability, Statistics and other areas of Mathematics.

In modern times, optimization problems are solved almost always with the aid of computational devices. However the previous mathematical analysis is the main responsible for the success of computational tools. Mathematical Analysis of optimization possess three fundamental aspects: (a) Analysis of structure of problems and families of problems; (b) Study and development of algorithms; (c) Specific manipulation of particular problems. Optimization groups in Brazil have advanced significantly along the three lines mentioned above.

The main mathematical tool for (a) is the so-called Convex Analysis, developed from the 60's, that allows the solution characterization of many problems, opening paths for the developments of practical algorithms. Complexity, convergence and stability of algorithms is analyzed in (b), taking into account, at the same time, their computational implementability. Finally, the approach in (c) is essentially interdisciplinar, because one tries, in practical situations, to formulate convenient models under the conditions of (a), for being solved with the techniques of (b).

Generally speaking, IMPA's group has worked more intensively along line (a) and Campinas' group has interesting contributions in (b), but both groups have developed research in the three main streams, including the resolution of practical problems. For the remaining groups (Florianópolis, S. Paulo) the distribution of the three main research branches is more or less uniform. Many researchers that studied in the main centers work presently in emergent centers such as Goiás, Piauí and Rio Preto.

The configuration of the area in Brazil is essentially similar to the international configuration. All the groups have intense contact with researchers of other countries, in particular from Latin America, especially Argentina, Chile and Venezuela. Several Latin-American students obtained their Ph.D. in optimization from Brazilian centers.