imported>Jlwoodwa: Adding short description: "Approximation for nonlinear optimization"

2024-09-14T23:40:41Z

Adding short description: "Approximation for nonlinear optimization"

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{{Short description|Approximation for nonlinear optimization}}
'''Successive Linear Programming''' ('''SLP'''), also known as '''Sequential Linear Programming''', is an [[optimization]] technique for approximately solving [[nonlinear optimization]] problems.<ref>{{harv|Nocedal|Wright|2006|p=551}}</ref> It is related to, but distinct from, [[Quasi-Newton method|quasi-Newton methods]].

Starting at some estimate of the optimal solution, the method is based on solving a sequence of first-order approximations (i.e. [[linearization]]s) of the model. The linearizations are linear programming problems, which can be solved efficiently. As the linearizations need not be bounded, [[trust region]]s or similar techniques are needed to ensure convergence in theory.
<ref>{{harv|Bazaraa |Sherali|Shetty|1993|p=432}}</ref>

SLP has been used widely in the [[petrochemical industry]] since the 1970s.<ref>{{harv|Palacios-Gomez|Lasdon|Enquist|1982}}</ref> Since then, however, they have been superseded by [[sequential quadratic programming]] methods. While solving a QP subproblem takes more time than solving an LP one, the overall decrease in the number of iterations, due to improved convergence, results in significantly lower running times and fewer function evaluations."

==See also==
* [[Sequential quadratic programming]]
* [[Sequential linear-quadratic programming]]
* [[Augmented Lagrangian method]]

==References==
{{Reflist}}

==Sources==
* {{Cite book | last1=Nocedal | first1=Jorge | last2=Wright | first2=Stephen J. | title=Numerical Optimization | publisher=[[Springer-Verlag]] | location=Berlin, New York | edition=2nd | isbn=978-0-387-30303-1 | year=2006 }}
* {{Cite book | last1=Bazaraa | first1=Mokhtar S. | last2=Sherali | first2=Hanif D. | last3=Shetty | first3=C.M. | title=Nonlinear Programming, Theory and Applications | publisher=[[John Wiley & Sons]] | edition=2nd | isbn=0-471-55793-5 | year=1993 }}
* {{Cite journal | last1=Palacios-Gomez| first1=F. | last2=Lasdon| first2=L. | last3=Enquist| first3=M. | title=Nonlinear Optimization by Successive Linear Programming | journal=Management Science | volume=28 | issue = 10 |date=October 1982 | pages=1106–1120 | doi=10.1287/mnsc.28.10.1106 }}

{{optimization algorithms|constrained}}

[[Category:Optimization algorithms and methods]]

{{algorithm-stub}}

Successive linear programming - Revision history

imported>Jlwoodwa: Adding short description: "Approximation for nonlinear optimization"