computer science

Successive linear programming

Successive linear programming is a computer science topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Successive linear programming rather than just read about it. In short: Successive Linear Programming (SLP), also known as Sequential Linear Programming, is an optimization technique for approximately solving nonlinear optimization problems. It is related to, but distinct from, quasi-Newton methods.

Key takeaways

Successive linear programming belongs to computer science; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Successive linear programming to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Successive linear programming from memory before moving on to harder problems.

Reference excerpt

Successive Linear Programming (SLP), also known as Sequential Linear Programming, is an optimization technique for approximately solving nonlinear optimization problems. It is related to, but distinct from, quasi-Newton methods. 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.

SLP has been used widely in the petrochemical industry since the 1970s. Since then, however, they have been superseded by sequential quadratic programming methods.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."

See also Sequential quadratic programming Sequential linear-quadratic programming Augmented Lagrangian method

References

Sources Nocedal, Jorge; Wright, Stephen J. (2006). Numerical Optimization (2nd ed.). Berlin, New York: Springer-Verlag. ISBN 978-0-387-30303-1. Bazaraa, Mokhtar S.; Sherali, Hanif D.; Shetty, C.M. (1993). Nonlinear Programming, Theory and Applications (2nd ed.). John Wiley & Sons. ISBN 0-471-55793-5. Palacios-Gomez, F.; Lasdon, L.; Enquist, M. (October 1982). "Nonlinear Optimization by Successive Linear Programming". Management Science. 28 (10): 1106–1120. doi:10.1287/mnsc.28.10.1106.

Worked examples

Example 1 — a first encounter with Successive linear programming

Start with the simplest possible case. Write down what Successive linear programming claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In computer science, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Successive linear programming before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Successive linear programming ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Successive linear programming

In research: Successive linear programming appears in computer science research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Successive linear programming in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Successive linear programming is common in secondary-school and first-year university syllabi. It links to neighbouring topics Algorithms and data structures stubs, Optimization algorithms and methods, so understanding it makes those chapters shorter.
In everyday life: Look for Successive linear programming outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Successive linear programming in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Successive linear programming means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Successive linear programming out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Successive linear programming in simple terms?

Why does Successive linear programming matter?

Because it connects several computer science ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Successive linear programming?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Successive linear programming.