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Be English-friendly or any other language-friendly means that UC is taught in a language but can either of the
following conditions:
1. There are support materials in English / other language;
2. There are exercises, tests and exams in English / other language;
3. There is a possibility to present written or oral work in English / other language.
1
3.0
0.0 h/sem
16.0 h/sem
0.0 h/sem
0.0 h/sem
0.0 h/sem
0.0 h/sem
0.0 h/sem
16.0 h/sem
68.0 h/sem
0.0 h/sem
84.0 h/sem
Since year
2019/2020
Pre-requisites
· Real analysis · Linear algebra
Objectives
Formulate and interpret mathematical models, in particular those arising from economics and finance. Determine, with critical judgment, which numerical methods to apply to solve each optimization problem.
Program
PC1. Introduction to MATLAB. PC2. Unconstrained optimization: (a) Necessary and sufficient conditions for the existence of optima. (b) Steppest descent and conjugate gradient. (c) Newton and quasi-Newton methods. PC3. Constrained optimiaztion: (a) KKT conditions. (b) Newton's method revisited. PC4. Applications.
Evaluation Method
Periodic assessment: · Home work (30 %) · Final exam (70 %), minimum grade equal to 7,5.
Teaching Method
The main learning process will be autonomous work through self-study and resolution of home work assignments (LM1). In class, there will be theoretical expositions of the main mathematical concepts and methods (LM2). The introduction to MATLAB will be made using work assignments and tutorials and the home work assignments (LM3).
Observations
Basic Bibliographic
· Nocedal, J. and Wright, St. "Numerical optimization", Springer Verlag (1999) . Bonnans, J.F et al, "Numerical Optimization: Theoretical and Practical Aspects" Springer Verlag (2006) . Izmailov, A. e Solodov, M. "Otimização" vols. 1 e 2 IMPA (2014)
Complementar Bibliographic
. Cornu éjols, G. et al. "Optimization in Finance" Cambridge University Press (2007) · Brandimarte, P. "Numerical Methods in Finance: A MATLAB-Based Introduction", Wiley- Interscience (2001).
