Successive linear programming

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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. The linearizations are linear programming problems, which can be solved efficiently. As the linearizations need not be bounded, trust regions or similar techniques are needed to ensure convergence in theory. ^[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, ISBN 0-471-55793-5.
^ Palacios-Gomez, F.; Lasdon, L.; Enquist, M. (1982), "Nonlinear Optimization by Successive Linear Programming", Management Science, 28 (10) {{citation}}: Unknown parameter |month= ignored (help)

External links

Optimization: Algorithms, methods, and heuristics

Unconstrained nonlinear

Functions

Gradients

Convergence	Trust region Wolfe conditions
Quasi–Newton	Berndt–Hall–Hall–Hausman Broyden–Fletcher–Goldfarb–Shanno and L-BFGS Davidon–Fletcher–Powell Symmetric rank-one (SR1)
Other methods	Conjugate gradient Gauss–Newton Gradient Mirror Levenberg–Marquardt Powell's dog leg method Truncated Newton

Hessians

Newton's method

Constrained nonlinear

General	Barrier methods Penalty methods
Differentiable	Augmented Lagrangian methods Sequential quadratic programming Successive linear programming

Convex optimization

Convex
minimization

Linear and
quadratic

Interior point	Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar
Basis-exchange	Simplex algorithm of Dantzig Revised simplex algorithm Criss-cross algorithm Principal pivoting algorithm of Lemke Active-set method