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Welcome to the Optimization & Applications Research Group
website.
Our
research group started in 1996 with the unofficial name of
"Research Group on Hydrothermal Optimization" under the
direction of Prof. Pedro M. Suárez. It received the official
accreditation as Research Group in 2013 under the name
"Optimization and Applications" (OPyAP, in Spanish), when it was
composed of 4 researchers: Pedro M. Suárez, Luis Bayón, José M.
Grau and María M. Ruiz. In 2016, three new researchers joined,
and at the same time, Prof. José M. Grau got in charge. At
present, the 7-member group is undergoing the quinquennial
preemptive re-evaluation.
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:
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- Functional Analysis
- Direct Methods (Ritz Method)
- Calculus of Variations
- Optimal Control (Pontryagin’s Principle, Bolza
Problem, Singular/Bang-Bang Control, Steady states,
Skiba points, etc.)
- Nonsmooth Analysis (Clarke’s generalized gradient,
etc.) |
Moreover, we have made significant contributions in the area of
Pure Mathematics, like for example in:
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- Problems Involving Inequality Constraints
- Differential Inclusions
- Broken Extremals
- Fields of Extremals
- Shooting Method
- Cyclic Coordinate Descent Algorithm
- Infimal Convolution
-
Combinatorial Optimization |
These mathematical problems arise from typical Engineering
problems, such as Optimization of Hydrothermal Systems, and also
from Economics problems. Among others, these include:
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- Equivalent Thermal Plant
- Economic Dispatch
- Multi-Fuel power plants
- Combined Cycle
units
- Minimization of Pollution Emissions (NOx,
SO2, ...)
- Environmentally Constrained Economic Dispatch
- Unit Commitment
- Short-Term Hydrothermal Coordination
- Pumped-storage plants
- Hydro-eolic
power plans
- Deregulated Electricity Market
- Forecasting Electricity Prices and wind generation
- Renewable and Non-Renewable
Resources
- Enzymatic chemical pathways
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Mathematical
Biosciences |
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