Successive linear programming

Successive Linear Programming (SLP), also known as Sequential Linear Programming, is an optimization technique for approximately solving nonlinear optimization problems.

Starting at some estimate of the optimal solution, the method is based on solving a sequence of first-order approximations (i.e. linearizations) of the model.

[3] Since then, however, they have been superseded by sequential quadratic programming methods.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."

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Graph of a strictly concave quadratic function with unique maximum.
Optimization computes maxima and minima.