Successive linear programming: Difference between revisions
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'''Successive Linear Programming''' ('''SLP''') is an extension of the technique of [[linear programming]] to allow the optimisation of [[nonlinear programming]] problems through a series of linear approximations. |
'''Successive Linear Programming''' ('''SLP''') is an extension of the technique of [[linear programming]] to allow the optimisation of [[nonlinear programming]] problems through a series of linear approximations. |
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Starting at some estimate of the optimal solution, the method is based on solving subsequent first order linearizations of the model. The |
Starting at some estimate of the optimal solution, the method is based on solving subsequent first order approximations (i.e. [[linearization|linearizations]]) of the model. The linearizations are linear programming problems, which can be solved efficiently. As the linearizations are often non-bounded by themselves, and also to handle cases when the optimum lies in the interior of the [[feasible region]], the method is typically applied with the combination of some step bounding technique like the [[trust region]] method. |
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<ref>{{Citation | last1=Bazaraa | first1=Mokhtar S. | last2=Sheraly | 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 | page=432 }}.</ref> |
<ref>{{Citation | last1=Bazaraa | first1=Mokhtar S. | last2=Sheraly | 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 | page=432 }}.</ref> |
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Revision as of 16:00, 22 March 2010
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| This article provides insufficient context for those unfamiliar with the subject. (October 2009) |
Successive Linear Programming (SLP) is an extension of the technique of linear programming to allow the optimisation of nonlinear programming problems through a series of linear approximations.
Starting at some estimate of the optimal solution, the method is based on solving subsequent first order approximations (i.e. linearizations) of the model. The linearizations are linear programming problems, which can be solved efficiently. As the linearizations are often non-bounded by themselves, and also to handle cases when the optimum lies in the interior of the feasible region, the method is typically applied with the combination of some step bounding technique like the trust region method. [1]
SLP, along with it's second order analog sequential quadratic programming is widely used for process engineering problems.
References
- ^ Bazaraa, Mokhtar S.; Sheraly, Hanif D.; Shetty, C.M. (1993), Nonlinear Programming, Theory and Applications (2nd ed.), John Wiley & Sons, p. 432, ISBN 0-471-55793-5.