Successive linear programming

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SLP - Successive Linear Programming

Linear programming is a powerful technique for optimisation but the requirement that all constraints be linear can make it difficult to write models that represent the real world closely enough to produce useful answers. Successive Linear Programming (SLP) is an extension of this technique which allows the optimisation of problems with non-linear characteristics as a series of linear approximations.

It is relatively easy to make a linear approximation to a nonlinear objective function and any nonlinear constraints, starting at some estimate of the optimal solution. This produces a linear program, which is solved to get an optimum and corresponding values of the variables.

A new linear approximation can now be made, and solved, and then the process repeated. The approach is thus similar conceptually to equation solving procedures which use linear approximations.

Unfortunately, because a linear program always finds its optimum on a constraint, if the optimum for the NLP is not in fact constrained, this method will not find it! Although it has some disadvantages, SLP may be an effective method if the optimum is known to lie on a constraint. There are even ways of making it work when the optimum is unconstrained, but this uses a concept known as a `trust region' and is not a commonly available technique.

SLP is not much used for process engineering problems, SQP, described below, is more usual.