Non-linear equations and numerical optimization¶
AA 2004/2005¶
Lessons of 21/3/2005 and 22/3/2005¶
One Dimensional Non-Linear Problems
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Lessons of 4/4/2005 and 5/4/2005¶
One-Dimensional Minimization
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Unconstrained minimization
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Lessons of 18/4/2005 and 19/4/2005¶
Conjugate Direction minimization
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Lessons of 2/5/2005 and 3/5/2005¶
Non-linear problems in N variable (preliminary draft)
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Quasi-Newton methods for minimization (preliminary draft)
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Lessons of 9/5/2005 and 10/5/2005¶
Trust Region Method (preliminary draft)
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Final exam task list¶
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 perform 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.