Linear Programming Program

Overview

This is a C++ console application designed to solve Linear Programming (LP) problems. The program takes a linear programming problem in any standard or non-standard form, converts it into a canonical form, and automatically applies the most suitable mathematical method to find the optimal solution.

Feature

1. Supports both MIN and MAX objective functions.
2. Handles various types of relational constraints (<=, >=, =) and automatically adjusts the matrix.
3. Offers an optional feature to print the dictionary (tableau) after every iteration loop to track the algorithm's progress.
4. Capable of identifying and notifying the user of special LP conditions such as Unbounded problems, Infeasible problems, and problems with Infinite solutions.

Algorithms

1. Standard Simplex Method: Used for standard canonical forms where all constant terms $b_i$ are non-negative.
2. Bland's Rule: Applied to prevent cycling when degeneracy is detected (e.g., when $b_i = 0$).
3. Two-Phase Simplex Method: Automatically triggered when auxiliary/artificial variables are needed, particularly when $b_i &lt; 0$ or when the constraints generate them.