Successive linear programming

Successive linear programming (SLP) methods solve a sequence of linear programming approximations to a nonlinear programming problem. Recall that if g,(x) is a nonlinear function and x° is the initial value for x, then the first two terms in the Taylor series expansion of gt(x) around x° are... 

The problem is to produce 50 MW from the two generators in such a way that the amount of fuel oil consumed is minimum. Use successive linear programming. 

One special type of optimization problem involving restrictions or constraints has been solved quite successfully by a technique known as linear programming. From a mathematical viewpoint the basic form of the problem may be stated very briefly. Consider a linear response function of n variables ... 

Two types of nonlinear optimizers—the sectionalized linear program and the gradient search—have been successfully implemented in advanced computer control schemes. 

An approach that has enjoyed industrial success is the application of sequential linear programming. The nonlinear problem is locally linearized, with bounds placed on the allowed moves for all the variables so that the local linearization is still appropriate. An iteration is to linearize, solve the corresponding linear program, move to the solution of the linear problem, and converge that solution to the solution of the nonlinear problem. This point is the start of the next iteration. Industry has used this approach successfully for a number of years. 

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