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 criterion, from some set of available alternatives. It is generally divided into two subfi ...
technique for approximately solving
nonlinear optimization
In mathematics, nonlinear programming (NLP) is the process of solving an optimization problem where some of the constraints or the objective function are nonlinear. An optimization problem is one of calculation of the extrema (maxima, minima or sta ...
problems.
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 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 study of dynamical systems, lineari ...
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, the ...
s or similar techniques are needed to ensure convergence in theory.
SLP has been used widely in the
petrochemical industry
The petrochemical industry is concerned with the production and trade of petrochemicals. A major part is constituted by the plastics (polymer) industry. It directly interfaces with the petroleum industry, especially the downstream sector.
Comp ...
since the 1970s.
See also
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Sequential quadratic programming
Sequential quadratic programming (SQP) is an iterative method for constrained nonlinear optimization. SQP methods are used on mathematical problems for which the objective function and the constraints are twice continuously differentiable.
SQP me ...
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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 ...
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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 a ...
References
Sources
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Optimization algorithms and methods
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