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Successive Linear Programming (SLP), also known as Sequential Linear Programming, is an optimization technique that can solve nonlinear optimization problems using Taylor series for approximate the non-linear objective function; if we take only the firsts two terms of Taylor serie, results a linear objective function that approximates the original objective. Therefore, we can solve the linear problem using the techniques of linear programming.
Starting at some estimate of the optimal solution, the method is based on solving the successive 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 has been widely in the petrochemical industry since the 1970s.[2]
References
^Bazaraa, Mokhtar S.; Sheraly, Hanif D.; Shetty, C.M. (1993), Nonlinear Programming, Theory and Applications (2nd ed.), John Wiley & Sons, p. 432, ISBN0-471-55793-5.
^Palacios-Gomez, F.; Lasdon, L.; Enquist, M. (1982), "Nonlinear Optimization by Successive Linear Programming", Management Science, 28 (10) {{citation}}: Unknown parameter |month= ignored (help)
