Tesis doctoral de Alberto Ferrer Biosca
This thesis has been motivated by the interest in applying deterministic global optimization procedures to problems in the real world with no special structures. We have focused on the short-term hydrothermal coordination of electricity generation problem (also named generation problem in this thesis) where the objective function and the nonlinear constraints are polynomials of degree up to four. In the generation problem there is no available d.C. Representation of the involved functions and we cannot take advantage of any special structure of the problem either. Hence, a very general problem, such as the above-mentioned, does not seem to have any mathematical structure conducive to computational implementations. Nevertheless, when f(x) is a continuous function and s is a nonempty closed set the problem can be transformed into an equivalent problem expressed by minimize l(z) subject to z 2 d n intc (canonical d.C. program), where l(z) is a convex function (which is usually a linear function) and d and c are closed convex sets. A mathematical complementary convex structure such as d n int c is not always apparent and even when it is explicit, a lot of work still remains to be done to bring it into a form amenable to e±cient computational implementations. The attractive feature of the mathematical complementary convex structure is that it involves convexity. Thus, we can use analytical tools from convex analysis like subdi(r)erential and supporting hyperplane. on the other hand, since convexity is involved in a reverse sense, these tools must be used in some specific way and combined with combinatorial tools like cutting planes, branch and bound and outer approximation. we introduce the common general mathematical complementary convex structure underlying in global optimization problems and describe the generation problem, whose functions are d.C. Functions because they are polynomials. thus, by using the properties of the d.C. Fu
Datos académicos de la tesis doctoral «Applicability of deterministic global optimization to the short-term hydrothermal coordination problem.«
- Título de la tesis: Applicability of deterministic global optimization to the short-term hydrothermal coordination problem.
- Autor: Alberto Ferrer Biosca
- Universidad: Politécnica de catalunya
- Fecha de lectura de la tesis: 30/03/2004
Dirección y tribunal
- Director de la tesis
- Narcis Nabona Francisco
- Tribunal
- Presidente del tribunal: Martínez legaz Juan enrique
- López cerdí marco Antonio (vocal)
- rosalind Elster (vocal)
- aris Daniilidis (vocal)