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A short review of
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Thesis Constrained, non-linear, derivative-free
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Noisy optimization
Contents
Constrained Optimization
Subsections
A short review of the available techniques.
Linear constraints
Active set - Null space method
Gradient Projection Methods
Non-Linear constraints
Penalty Methods
Barrier Methods
Primal-dual interior point
Duality
Lower Bounds on optimal value
The Lagrange dual problem of a linear problem in inequality form
A primal-dual Algorithm
Central path
Link between Barrier method and Interior point method
A final note on primal-dual algorithms.
SQP Methods
A small note about the H matrix in the SQP algorithm.
A final note about the SQP algorithm.
The final choice of a constrained algorithm
Detailed description of the constrained step
The QP algorithm
Equality constraints
Active Set methods
Duality in QP programming
A note on the implemented QP
The SQP algorithm
Length of the step.
Maratos effect: The SOC step.
Update of
Stopping condition
The SQP in detail
The constrained step in detail
Remarks about the constrained step.
Numerical Results for the constrained algorithm
The METHOD project
Parametrization of the shape of the blades
Preliminary research
Preliminary numerical results
Interface between CONDOR and XFLOS / Pre-Solve phase
Config file on client node
Conclusions
About the code
Improvements
Unconstrained case
Constrained case
Some advice on how to use the code.
The H-norm
Annexes
Line-Search addenda.
Speed of convergence of Newton's method.
Note
How to improve Newton's method : Zoutendijk Theorem.
Angle test.
The ``steepest descent'' trick.
Gram-Schmidt orthogonalization procedure.
Algorithm 1.
Algorithm 2.
Notions of constrained optimization
The secant equation
1D Newton's search
Newton's method for non-linear equations
Cholesky decomposition.
Performing
decomposition.
Performing Cholesky decomposition.
QR factorization
A simple direct optimizer: the Rosenbrock optimizer
Code
Rosenbrock's optimizer
rosenbrock.cpp
rosenbrock.h
testR1.cpp
AMPL files
hs022
hs023
hs026
hs034
hs038
hs044
hs065
hs076
hs100
hs106
hs108
hs116
hs268
Frank Vanden Berghen 2004-04-19
decomposition.