Numerical Unconstrained Optimization

AA 2007/2008

Lessons of 8/5/2008

One Dimensional Non-Linear Problems

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One-Dimensional Minimization

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Lessons of 9/5/2008

Unconstrained minimization

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Lessons of 15/5/2008

Conjugate Direction minimization

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Lessons of 23/5/2008

Non-linear problems in n variable

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Lessons of 29/5/2008

Quasi-Newton methods for minimization

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Lessons of 6/6/2008 and 12/6/2008

Trust Region methods

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Some MATLAB codes for minimization

Codes

All MATLAB file sin a unique archive Codici.zip

The possible tasks

  • The Preconditioned Conjugate Gradient method

  • The Fletcher Reeves and Polack Ribiere method

  • The Broyden method for system of nonlinear equations

  • The SR1 method for uncostrained optimization

  • The DFP and BFGS method for uncostrained optimization

  • The double dogleg method

  • The exact trust region method

  • The Levemberg-Marquardt method

  • The Sequential Quadratic Programming (SQP) method

  • The multidimensional Newton method and the Kantorovich proofs of its local quadratic convergence

The candidate must choose an argument and permorm the following task:

  • Search in the literature to obtain a list of significative reference (10-20 reference)

  • Write a report describing the argument

  • Write a C++ code implementing the algorithm

The code should be commented in the report, or in alternative well documented using e.g. DOXIGEN.