Numerical Unconstrained Optimization¶
AA 2007/2008¶
Lessons of 8/5/2008¶
One Dimensional Non-Linear Problems
full screen version slides-1D-1x1.pdf
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One-Dimensional Minimization
full screen version slides-m1D-1x1.pdf
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Lessons of 9/5/2008¶
Unconstrained minimization
full screen version slides-mND-1x1.pdf
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Lessons of 15/5/2008¶
Conjugate Direction minimization
full screen version slides-CG-1x1.pdf
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Lessons of 23/5/2008¶
Non-linear problems in n variable
full screen version slides-ND-1x1.pdf
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Lessons of 29/5/2008¶
Quasi-Newton methods for minimization
full screen version slides-mQN-1x1.pdf
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Lessons of 6/6/2008 and 12/6/2008¶
Trust Region methods
full screen version slides-TR-1x1.pdf
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Some MATLAB codes for minimization
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.