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

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

Software

https://simtk.org/home/lapack

http://www.gurobi.com/

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://scicomp.stackexchange.com/questions/83/is-there-a-high-quality-nonlinear-programming-solver-for-python

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

SciPy functions:

http://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.fmin.html#scipy.optimize.fmin

http://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.minimize.html#scipy.optimize.minimize

Cobyla:

http://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.fmin_cobyla.html#scipy.optimize.fmin_cobyla

• Constrained optimization with inequality constraints
• Variable bounds and equality constraints not explicitly supporte (must be implemented as inequality constraints).

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/