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Add Primal-Dual Interior-Point Method for linear programming
Describe your change:
- [x] Add an algorithm
- [ ] Fix a bug or typo in an existing algorithm?
- [ ] Add or change doctests? -- Note: Please avoid changing both code and tests in a single pull request.
- [ ] Documentation change?
Checklist:
- [x] I have read CONTRIBUTING.md.
- [x] This pull request is all my own work -- I have not plagiarized.
- [x] I know that pull requests will not be merged if they fail the automated tests.
- [x] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
- [x] All new Python files are placed inside an existing directory.
- [x] All filenames are in all lowercase characters with no spaces or dashes.
- [x] All functions and variable names follow Python naming conventions.
- [x] All function parameters and return values are annotated with Python type hints.
- [x] All functions have doctests that pass the automated testing.
- [x] All new algorithms include at least one URL that points to Wikipedia or another similar explanation.
- [ ] If this pull request resolves one or more open issues then the description above includes the issue number(s) with a closing keyword: "Fixes #ISSUE-NUMBER".
Description of the change:
This pull request adds an implementation of the Primal-Dual Interior-Point Method for solving linear programming problems. The method handles >=, <=, and = constraints and ensures each variable x1, x2, ... >= 0.
Changes:
- Added
InteriorPointMethodclass to solve linear programming problems using the Primal-Dual Interior-Point Method. - Included methods for validating input, converting constraints to standard form, and solving the linear programming problem.
- Provided a main execution block to demonstrate the usage of the class.
Testing:
- The implementation has been tested with a sample problem in the main execution block.
References:
- https://en.wikipedia.org/wiki/Interior-point_method