Successive Linear Programming (SLP), also known as Sequential Linear Programming, is an
optimization
Mathematical optimization (alternatively spelled ''optimisation'') or mathematical programming is the selection of a best element, with regard to some criteria, from some set of available alternatives. It is generally divided into two subfiel ...
technique for approximately solving
nonlinear optimization
In mathematics, nonlinear programming (NLP) is the process of solving an optimization problem where some of the constraints are not linear equalities or the objective function is not a linear function. An optimization problem is one of calculation ...
problems. It is related to, but distinct from,
quasi-Newton methods
In numerical analysis, a quasi-Newton method is an Iterative method, iterative numerical method used either to Root-finding algorithm, find zeroes or to Mathematical optimization, find local maxima and minima of functions via an iterative recurren ...
.
Starting at some estimate of the optimal solution, the method is based on solving a sequence of first-order approximations (i.e.
linearization
In mathematics, linearization (British English: linearisation) is finding the linear approximation to a function at a given point. The linear approximation of a function is the first order Taylor expansion around the point of interest. In the ...
s) of the model. The linearizations are linear programming problems, which can be solved efficiently. As the linearizations need not be bounded,
trust region
In mathematical optimization, a trust region is the subset of the region of the objective function that is approximated using a model function (often a quadratic). If an adequate model of the objective function is found within the trust region, th ...
s or similar techniques are needed to ensure convergence in theory.
SLP has been used widely in the
petrochemical industry
file:Jampilen Petrochemical Co. 02.jpg, 300px, Jampilen Petrochemical co., Asaluyeh, Iran
The petrochemical industry is concerned with the production and trade of petrochemicals. A major part is constituted by the plastics industry, plastics (poly ...
since the 1970s.
Since then, however, they have been superseded by
sequential quadratic programming
Sequential quadratic programming (SQP) is an iterative method for constrained nonlinear optimization, also known as Lagrange-Newton method. SQP methods are used on mathematical problems for which the objective function and the constraints are twi ...
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."
See also
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Sequential quadratic programming
Sequential quadratic programming (SQP) is an iterative method for constrained nonlinear optimization, also known as Lagrange-Newton method. SQP methods are used on mathematical problems for which the objective function and the constraints are twi ...
*
Sequential linear-quadratic programming
Sequential linear-quadratic programming (SLQP) is an iterative method for nonlinear optimization problems where objective function and constraints are twice continuously differentiable. Similarly to sequential quadratic programming (SQP), SLQP pr ...
*
Augmented Lagrangian method
Augmented Lagrangian methods are a certain class of algorithms for solving constrained optimization problems. They have similarities to penalty methods in that they replace a constrained optimization problem by a series of unconstrained problems ...
References
Sources
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Optimization algorithms and methods
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