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PM-2011-1-handout - Programao Matemtica Programao Matemtica...

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Programação Matemática Programação Matemática AULA 1 Universidade de Aveiro 2010/2011 http://elearning.ua.pt
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Programação Matemática Introduction Apresentação da disciplina Docente: Tatiana Tchemisova Cordeiro [email protected] Gab. 11. 3.51 Aulas: Terças feiras das 14.00 até 17.00 Atendimento: Sextas feira das 14.00 até 18.00
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Programação Matemática Introduction Bibliografia I Bazaraa, M.S., Sherali, H.D. , Shetty C.M. Nonliner Programming. Theory and Algorithms. (2 a edição) John Wiley Sons, Inc. , (1993) I Luenberger, D.G. , Introduction to Linear and Nonlinear Programming. Addison-Wesley Publishing Company (1973). I Miller R.E. , Optimization: Foundations and Applications. John Wiley Sons, Inc., (2000) I Snyman J.A. , Practical Mathematical Optimization: An Introduction to Basic Optimization Theory and Classical and New Gradient-based Algorithms . Springer, (2005) I Mangasarian O.L. , Nonlinear Programming. McGraw-Hill (1969)
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Programação Matemática Introduction Bibliografia I Karlin S. , Mathematical Methods and Theory in Games, Programming, and Economics . Vol.II, Addison-Wesley, Mass (1959) I Rockafellar R.T. , Convex Analysis Prinseton University Press, Princeton, N.J. (1970) I Nash S.G., Sofer A. , Linear and Nonlinear Programming . McGraw-Hill (1996) I Karmanov V.G. , Mathematical Programming . MIR, Moscow (1986) I Nemirovski A. , Five Lections on Modern Convex Optimization, C.O.R.E. Summer School on Modern Convex Optimization , August 26-30, 2002 http://iew3. technion.ac.il/Home/Users/Nemirovski.phtml
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Programação Matemática Introduction Bibliografia I Bertsekas D.P. , Nondifferential Optimization . North Holland Publishing Company, Amsterdam, (1975) I Gill Ph.E., Murray W., Wright M.H. , Practical Optimization . Academic Press. (1981) I Nocedal J.,Wright S.J. , Numerical Optimization . Springer (1999) I Peressini, A.L., Sullivan, F.E. e Uhl, Jr.J.J. , The Mathematics of Nonlinear Programming , Springer-Verlag. (1993) I Brinkhuis J., Tikhomirov V. , Optimization: Insights and Applications , Princeton University Press. (1995) I Gill Ph.E., Murray W., Wright M.H. , Practical Optimization . Academic Press. (1981)
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Programação Matemática Introduction Problema Geral de Programação Matemática min x X f ( x ) . Aqui f – função objectivo; X R – conjunto admissível. Conforme a representação do conjunto admissível X , podemos obter problema de 1. Programação Linear 2. Programação Não Linear 3. Programação Convexa 4. Programação Cónica 5. Programação Semi-infinita 6. Programação Semidefinida 7. ...
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Programação Matemática Introduction Processo de Optimização I Modelação do problema aplicado na forma do problema de Optimização; I Aplicação da Teoria de Optimização: focar na existência, unicidade de soluções óptimas e na sua caracterização; I Aplicação de um Método de Optimização computacional adequado para o problema dado; I Testes computacionais , análise dos resultados obtidos e comparação com as previsões teóricas e os outros resultados acessíveis.
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Programação Matemática Introduction Histórico 1939– Leonid Kantorovich formula problema de Programação Linear; 1947 – George Dantzig publica o artigo sobre o Método Simplex ;
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