# integer programming

Published articles for integer programming.

This is one page of public article previews, not the complete archive. Follow Next page to continue. Summaries are not the original full articles.

## Optimization Models for Subset Cover

DevFeed: [Optimization Models for Subset Cover](<https://devfeed.tech/articles/optimization-models-for-subset-cover-40441.md>)

Original publisher: [Read original article](<https://www.jeremykun.com/2020/10/20/optimization-models-for-subset-cover/>)

Published: 2020-10-20T09:00:00Z

Content type: article

Language: en

Sources: [Jeremy Kun](<https://devfeed.tech/sources/jeremy-kun.md>)

Topics: [Optimization](<https://devfeed.tech/topics/optimization.md>), [Code](<https://devfeed.tech/topics/code.md>), [Open Source](<https://devfeed.tech/topics/open-source.md>)

Tags: [article](<https://devfeed.tech/tags/article.md>), [boolean-satisfiability](<https://devfeed.tech/tags/boolean-satisfiability.md>), [combinatorics](<https://devfeed.tech/tags/combinatorics.md>), [integer-programming](<https://devfeed.tech/tags/integer-programming.md>), [mathematics](<https://devfeed.tech/tags/mathematics.md>), [optimization](<https://devfeed.tech/tags/optimization.md>), [programming](<https://devfeed.tech/tags/programming.md>), [python](<https://devfeed.tech/tags/python.md>), [smt](<https://devfeed.tech/tags/smt.md>), [source](<https://devfeed.tech/tags/source.md>), [subset-cover](<https://devfeed.tech/tags/subset-cover.md>), [z3](<https://devfeed.tech/tags/z3.md>)

### AI overview

This article explores subset covering as a combinatorial optimization problem and compares Integer Linear Programming solvers with Z3, an open-source SMT solver from Microsoft. It defines a generalized formulation for covering all subsets of size l with the fewest subsets of size k.

### Source excerpt

In a recent newsletter article I complained about how researchers mislead about the applicability of their work. I gave SAT solvers as an example. People provided interesting examples in response, but what was new to me was the concept of SMT (Satisfiability Modulo Theories), an extension to SAT. SMT seems to have more practical uses than vanilla SAT (see the newsletter for details). I wanted to take some time to explore SMT solvers, and I landed on Z3, an open-source SMT solver from Microsoft.

## Linear Programming and the Simplex Algorithm

DevFeed: [Linear Programming and the Simplex Algorithm](<https://devfeed.tech/articles/linear-programming-and-the-simplex-algorithm-40371.md>)

Original publisher: [Read original article](<https://www.jeremykun.com/2014/12/01/linear-programming-and-the-simplex-algorithm/>)

Published: 2014-12-01T10:00:59Z

Content type: tutorial

Language: en

Sources: [Jeremy Kun](<https://devfeed.tech/sources/jeremy-kun.md>)

Topics: [Algorithm](<https://devfeed.tech/topics/algorithm.md>), [Programming](<https://devfeed.tech/topics/programming.md>)

Tags: [algorithm](<https://devfeed.tech/tags/algorithm.md>), [code](<https://devfeed.tech/tags/code.md>), [exponential-time-algorithms](<https://devfeed.tech/tags/exponential-time-algorithms.md>), [integer-programming](<https://devfeed.tech/tags/integer-programming.md>), [linear-algebra](<https://devfeed.tech/tags/linear-algebra.md>), [linear-programming](<https://devfeed.tech/tags/linear-programming.md>), [lp-relaxation](<https://devfeed.tech/tags/lp-relaxation.md>), [optimization](<https://devfeed.tech/tags/optimization.md>), [programming](<https://devfeed.tech/tags/programming.md>), [row-reduction](<https://devfeed.tech/tags/row-reduction.md>), [simplex-algorithm](<https://devfeed.tech/tags/simplex-algorithm.md>)

### AI overview

This tutorial explains how to implement the simplex algorithm for solving linear programs. It introduces standard form and shows how slack variables convert inequality constraints into equality constraints.

### Source excerpt

In the last post in this series we saw some simple examples of linear programs, derived the concept of a dual linear program, and saw the duality theorem and the complementary slackness conditions which give a rough sketch of the stopping criterion for an algorithm. This time we'll go ahead and write this algorithm for solving linear programs, and next time we'll apply the algorithm to an industry-strength version of the nutrition problem we saw last time.