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The Sequential Quadratic Programming (SQP) that I am talking about is based on here. And the Sequential Least SQuares Programming (SLSQP) is based on SciPy documentation

gung - Reinstate Monica
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Nicholas
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  • I don't have access to algorithm documentation, so I really don't know what Sequential Least SQuares Programming is. The link https://github.com/stevengj/nlopt/tree/master/slsqp may give a bit of a guess. That said, Sequential Quadratic Programming describes a family of algorithms of which there are many variants, differing in such things as use of trust regions vs. line search, use of actual Hessian (Newton) vs. Quasi-Newton (Newton), and many other important details. – Mark L. Stone Mar 18 '17 at 16:18
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    The Scipy docs say that they use an implementation described in "A software package for sequential quadratic programming", so I would assume they mean the same thing. Least squares is a quadratic problem. – AaronDefazio Mar 30 '17 at 05:54
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    They are the same. Check out this link http://degenerateconic.com/slsqp/ – MisterHoud Aug 05 '19 at 16:44
  • Welcome to the site. At present this is more of a comment than an answer. You could expand it, perhaps by giving a summary of the information at the link, or we can convert it into a comment for you. – gung - Reinstate Monica Aug 05 '19 at 17:02

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Actually SQP and SLSQP sovles the same subproblem of Quadratic Programming (QP) (see subproblem here) on each algorithm step.

  • In SQP the problem of QP is solved by methods of Quadratic Programming.

  • In SLSQP to solve the problem of QP you should $LDL^{-1}$-factorize Lagrange Hessian and then solve a linear least squares problem.

Least Squares Subproblem

Check the article:

Kraft, D. A software package for sequential quadratic programming. 1988. Tech. Rep. DFVLR-FB 88-28, DLR German Aerospace Center -- Institute for Flight Mechanics, Koln, Germany.

Mary Samodelkina
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