User:Jarle Pahr/Optimization

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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

Fractional linear programming

http://www.joptimizer.com/linearFractionalProgramming.html

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

Fractional quadratic programming

http://www.sciencedirect.com/science/article/pii/S0377221705003243#

http://www.sciencedirect.com/science/article/pii/S0377221705006661

http://www.sciencedirect.com/science/article/pii/S0377221701002624

http://www.sciencedirect.com/science/article/pii/S0096300309001398


http://books.google.no/books?id=1a6lSRbQ4YsC&pg=PA1081&lpg=PA1081&dq=multi-ratio+fractional+programming&source=bl&ots=ZOkVz-EAoV&sig=LnOGVMiu2_5sP5eyzFmYTm3s7NU&hl=no&sa=X&ei=K6r4UsbpFKe6ygOnyICYBQ&ved=0CIYBEOgBMAc#v=onepage&q=multi-ratio%20fractional%20programming&f=false

Convex optimization

Boyd: Convex Optimization: http://www.stanford.edu/~boyd/cvxbook/bv_cvxbook.pdf

https://class.stanford.edu/courses/Engineering/CVX101/Winter2014/about

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

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

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

http://nlpy.sourceforge.net/

Pyomo:

https://software.sandia.gov/trac/coopr/wiki/Pyomo

CVXOPT

http://cvxopt.org/

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

http://pic.dhe.ibm.com/infocenter/cplexzos/v12r5/index.jsp?topic=%2Fcom.ibm.cplex.zos.help%2FFileFormats%2Ftopics%2FMPS_example.html

http://docs.mosek.com/6.0/pyapi/node021.html

http://lpsolve.sourceforge.net/5.0/mps-format.htm

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/

Convexity and Optimization in Banach Spaces: http://www.springer.com/mathematics/book/978-94-007-2246-0

Discussion

http://forum.openopt.org/viewforum.php?id=20