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References

Origin of the algorithms

The algorithms implemented in this package were developed by Prof. Dr. K. Schittkowski and co-authors. The sources of this package were written from scratch from the published user's guides and papers listed below; no source code of the original implementations was used.

Sequential quadratic programming

  1. Schittkowski K. (1985/86): NLPQL: A Fortran subroutine solving constrained nonlinear programming problems, Annals of Operations Research, Vol. 5, 485-500
  2. Schittkowski K. (1983): On the convergence of a sequential quadratic programming method with an augmented Lagrangian line search function, Mathematische Operationsforschung und Statistik, Series Optimization, Vol. 14, 197-216
  3. Schittkowski K. (1981): The nonlinear programming method of Wilson, Han and Powell. Part 1: Convergence analysis, Numerische Mathematik, Vol. 38, 83-114
  4. Schittkowski K. (1981): The nonlinear programming method of Wilson, Han and Powell. Part 2: An efficient implementation with linear least squares subproblems, Numerische Mathematik, Vol. 38, 115-127
  5. Powell M.J.D. (1978): The convergence of variable metric methods for nonlinearly constrained optimization calculations, in: Nonlinear Programming 3, Academic Press
  6. Boggs P.T., Tolle J.W. (1995): Sequential quadratic programming, Acta Numerica, Vol. 4, 1-51
  1. Dai Y.H., Schittkowski K. (2008): A sequential quadratic programming algorithm with non-monotone line search, Pacific Journal of Optimization, Vol. 4, 335-351
  2. Schittkowski K. (2009/2015): NLPQLP: A Fortran implementation of a sequential quadratic programming algorithm with distributed and non-monotone line search - User's guide, Version 4.2, Report, Department of Computer Science, University of Bayreuth
  3. Schittkowski K. (2011): A robust implementation of a sequential quadratic programming algorithm with successive error restoration, Optimization Letters, Vol. 5, 283-296
  4. Grippo L., Lampariello F., Lucidi S. (1986): A non-monotone line search technique for Newton's method, SIAM Journal on Numerical Analysis, Vol. 23, 707-716
  5. Armijo L. (1966): Minimization of functions having Lipschitz continuous first partial derivatives, Pacific Journal of Mathematics, Vol. 16, 1-3

Quadratic programming

  1. Goldfarb D., Idnani A. (1983): A numerically stable method for solving strictly convex quadratic programs, Mathematical Programming, Vol. 27, 1-33
  2. Powell M.J.D. (1983): ZQPCVX, a FORTRAN subroutine for convex quadratic programming, Report DAMTP/1983/NA17, University of Cambridge
  3. Schittkowski K. (2011): QL: A Fortran code for convex quadratic programming - User's guide, Report, Department of Computer Science, University of Bayreuth

Many constraints and further variants

  1. Schittkowski K. (2010): NLPQLB: A Fortran implementation of an SQP algorithm with active set strategy for solving optimization problems with a very large number of nonlinear constraints - User's guide, Report, Department of Computer Science, University of Bayreuth
  2. Schittkowski K. (2012): NLPQLY: An easy-to-use Fortran implementation of a sequential quadratic programming algorithm - User's guide, Report, Department of Computer Science, University of Bayreuth
  3. Schittkowski K. (2009): An active set strategy for solving optimization problems with up to 200,000,000 nonlinear constraints, Applied Numerical Mathematics, Vol. 59, 2999-3007

Test problems

  1. Hock W., Schittkowski K. (1981): Test Examples for Nonlinear Programming Codes, Lecture Notes in Economics and Mathematical Systems, Vol. 187, Springer
  2. Schittkowski K. (1987): More Test Examples for Nonlinear Programming, Lecture Notes in Economics and Mathematical Systems, Vol. 282, Springer
  3. Hock W., Schittkowski K. (1983): A comparative performance evaluation of 27 nonlinear programming codes, Computing, Vol. 30, 335-358
  4. Tanaka Y., Fukushima M., Ibaraki T. (1988): A globally convergent SQP method for semi-infinite nonlinear optimization, Journal of Computational and Applied Mathematics, Vol. 23, 141-153
  5. Bongartz I., Conn A.R., Gould N., Toint Ph. (1995): CUTE: Constrained and unconstrained testing environment, ACM Transactions on Mathematical Software, Vol. 21, No. 1, 123-160