User:Jarle Pahr/Optimization: Difference between revisions
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*Constrained optimization with inequality constraints | *Constrained optimization with inequality constraints | ||
*Variable bounds and equality constraints not explicitly supporte (must be implemented as inequality constraints). | *Variable bounds and equality constraints not explicitly supporte (must be implemented as inequality constraints). | ||
Sequential Least SQuares Programming (SLSQP): | |||
Global solvers: | Global solvers: |
Revision as of 14:13, 13 January 2014
Notes on optimization theory:
Numerical recipes: http://www.nr.com/
See also http://openwetware.org/wiki/Optimality_In_Biology
Numerical optimization of industrial processes: http://support.dce.felk.cvut.cz/mediawiki/images/5/50/Bp_2013_caletkova_lenka.pdf
http://scipy-lectures.github.io/advanced/mathematical_optimization/index.html
Concepts
Pareto front:
Linear programming:
http://www.aimms.com/aimms/download/manuals/aimms3om_linearprogrammingtricks.pdf
Quadratic programming:
Convex optimization:
http://systemsbiology.ucsd.edu/Classes/Convex
Algorithms
Software
GLPK
http://sourceforge.net/projects/minion/?source=directory
OpenOpt: http://openopt.org/Welcome
Python
http://docs.scipy.org/doc/scipy/reference/tutorial/optimize.html
http://www.mcs.anl.gov/research/projects/tao/index.html
https://bitbucket.org/dalcinl/tao4py
https://wiki.python.org/moin/PythonForOperationsResearch
SciPy functions:
http://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.fmin.html#scipy.optimize.fmin
Cobyla:
- Constrained optimization with inequality constraints
- Variable bounds and equality constraints not explicitly supporte (must be implemented as inequality constraints).
Sequential Least SQuares Programming (SLSQP):
Global solvers:
http://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.brute.html#scipy.optimize.brute
Constrained optimization
http://www.mit.edu/~dimitrib/Constrained-Opt.pdf
http://www.mathworks.se/help/optim/constrained-optimization.html
http://en.wikipedia.org/wiki/Constrained_optimization
Least-squares minimization
http://www.math.ntnu.no/~hek/Optimering2010/LeastSquaresOptimization2010.pdf
http://en.wikipedia.org/wiki/Least_squares
http://math.stackexchange.com/questions/69613/linear-least-squares-with-inequality-constraints
http://www.ppsw.rug.nl/~kiers/leastsquaresbook.pdf
Least squares optimization: http://www.cns.nyu.edu/~eero/NOTES/leastSquares.pdf
From the above: "Least squares (LS) problems are optimization problems in which the objective (error) function may be expressed as a sum of squares."
Bibliography
Books:
Convex Optimization – Boyd and Vandenberghe: http://www.stanford.edu/~boyd/cvxbook/