Welcome to the Optimization & Applications Research Group
website. Our research activities focus primarily on the field of
Optimization, more specifically on Dynamic Optimization and
Quadratic Programming. We also apply these techniques to several
real practical problems, mainly in Hydrothermal Systems, but
also in Economics and Chemistry, among other fields. Due to the
hybrid nature of the research that we carry out, we publish our
work not only in Applied Mathematics forums, but also in
Engineering forums.
We approach these problems from a mathematical perspective,
using diverse tools such as:
 Functional Analysis
 Direct Methods (Ritz Method)
 Calculus of Variations
 Optimal Control (Pontryagin’s Principle, Bolza
Problem, Singular/BangBang Control, etc.)
 Nonsmooth Analysis (Clarke’s generalized gradient,
etc.) 
Moreover, we have made significant contributions in the area of
Pure Mathematics, like for example in:
 Problems Involving Inequality Constraints
 Differential Inclusions
 Broken Extremals
 Fields of Extremals
 Shooting Method
 Cyclic Coordinate Descent Algorithm
 Infimal Convolution 
These mathematical problems arise from typical Engineering
problems, such as Optimization of Hydrothermal Systems, and also
from Economics problems. Among others, these include:
 Equivalent Thermal Plant
 Economic Dispatch
 MultiFuel power plants
 Combined Cycle
units
 Minimization of Pollution Emissions (NO_{x},
SO_{2}, ...)
 Environmentally Constrained Economic Dispatch
 Unit Commitment
 ShortTerm Hydrothermal Coordination
 Pumpedstorage plants
 Hydroeolic
power plans
 Deregulated Electricity Market
 Forecasting Electricity Prices and wind generation
 Renewable and NonRenewable
Resources
 Linear unbranched
chemical process

Mathematical
Biosciences 
