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Revision as of 04:38, 4 February 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
Categories
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."
Linear programming
http://www.aimms.com/aimms/download/manuals/aimms3om_linearprogrammingtricks.pdf
Bi-level programming
http://coral.ie.lehigh.edu/~ted/files/papers/ScottDeNegreDissertation11.pdf
http://users.isy.liu.se/johanl/yalmip/pmwiki.php?n=Tutorials.BilevelProgramming
http://www.or.ms.unimelb.edu.au/handouts/Bilevel.pdf
Quadratic programming
Convex optimization
http://systemsbiology.ucsd.edu/Classes/Convex
Concepts
Pareto front:
http://en.wikipedia.org/wiki/Karush%E2%80%93Kuhn%E2%80%93Tucker_conditions
Algorithms
- Nelder-Mead
- COBYLA
Software
http://wiki.mcs.anl.gov/leyffer/images/7/75/NLP-Solvers.pdf
Commercial
Open source
http://www.mcs.anl.gov/research/projects/tao/index.html
https://bitbucket.org/dalcinl/tao4py
https://wiki.python.org/moin/PythonForOperationsResearch
SciPy
See http://openwetware.org/wiki/User:Jarle_Pahr/SciPy#Optimization
PyOpt
http://www.pyopt.org/index.html
PyOpt reference: http://www.pyopt.org/reference/index.html
Sequential Least Squares Programming (SLSQP): http://www.pyopt.org/reference/optimizers.slsqp.html
COBYLA: http://www.pyopt.org/reference/optimizers.cobyla.html
SDPEN - Sequential Penalty Derivative-free method for Nonlinear constrained optimization: http://www.pyopt.org/reference/optimizers.sdpen.html
CONMIN - CONstrained function MINimization: http://www.pyopt.org/reference/optimizers.conmin.html
NLPy
Pyomo:
https://software.sandia.gov/trac/coopr/wiki/Pyomo
CVXOPT
OpenOpt
http://openopt.org/Welcome Fmincon: http://openopt.org/fmincon
File formats
MPS: http://en.wikipedia.org/wiki/MPS_%28format%29
http://www.cenapad.unicamp.br/parque/manuais/OSL/oslweb/features/featur11.htm
http://plato.asu.edu/cplex_mps.pdf
http://miplib.zib.de/miplib3/mps_format.txt
Duality theory
http://en.wikipedia.org/wiki/Duality_%28optimization%29
http://en.wikipedia.org/wiki/Linear_programming#Duality
http://en.wikipedia.org/wiki/Duality_gap
http://en.wikipedia.org/wiki/Weak_duality
http://en.wikipedia.org/wiki/Strong_duality
Bibliography
Books:
Convex Optimization – Boyd and Vandenberghe: http://www.stanford.edu/~boyd/cvxbook/