User:Jarle Pahr/Optimization

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

http://www.tu-ilmenau.de/fileadmin/media/simulation/Lehre/Vorlesungsskripte/Lecture_materials_Abebe/QPs_with_IPM_and_ASM.pdf

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

Convex optimization

http://systemsbiology.ucsd.edu/Classes/Convex

Concepts

Pareto front:

Algorithms

• Nelder-Mead
• COBYLA

Software

Commercial

• https://simtk.org/home/lapack
• http://www.gurobi.com/

Open source

• GLPK
• http://sourceforge.net/projects/minion/?source=directory
• OpenOpt: http://openopt.org/Welcome

SciPy

See http://openwetware.org/wiki/User:Jarle_Pahr/SciPy#Optimization

http://www.mcs.anl.gov/research/projects/tao/index.html

https://bitbucket.org/dalcinl/tao4py

http://mdolab.engin.umich.edu/content/pyopt-python-based-object-oriented-framework-nonlinear-constrained-optimization-0

https://wiki.python.org/moin/PythonForOperationsResearch

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

Bibliography

Books:

Convex Optimization – Boyd and Vandenberghe: http://www.stanford.edu/~boyd/cvxbook/