Update README.md

README.md

@@ -2,61 +2,43 @@
 ## IPM Solver for BCP in LP
 
 ### Description
-
-This project implements an Interior Point Method (IPM) solver for Branch-Cut-Price (BCP) in Linear Programming (LP). It is designed to efficiently solve large-scale LP problems using advanced numerical techniques. The solver is crafted as a library for use in Python, leveraging the capabilities of pybind11.
+IPyM is a Python-based Interior Point Method (IPM) solver tailored for Branch-Cut-Price (BCP) in Linear Programming (LP). It efficiently tackles large-scale LP problems using advanced numerical techniques and integrates seamlessly with Python through pybind11.
 
 ### Dependencies
+- **Eigen**: A versatile C++ template library for linear algebra.
+- **Cholmod**: Specialized in solving sparse linear systems.
+- **pybind11**: Facilitates C++ and Python interoperability.
 
- - Eigen: A C++ template library for linear algebra.
- - Cholmod: A library for solving sparse linear systems.
- - pybind11: A lightweight header-only library that exposes C++ types in Python and vice versa.
-
-To ensure full functionality, make sure these dependencies are properly installed and configured in your environment.
+*Ensure these dependencies are installed and configured in your environment for optimal functionality.*
 
 ### Solving Method
-
-The *AUGMENTED* definition changes the compilation to use an augmented matrix form.
+Utilize the *AUGMENTED* definition to compile with an augmented matrix form.
 
 ### Installation
-
-To install this project, follow these steps:
-
- - Install CMake, which will be used to build the project.
- - Clone the repository: git clone [repository-url].
- - Navigate to the project directory: cd [project-directory].
- - Create a build directory and navigate into it: mkdir build && cd build.
- - Run CMake to configure the project: cmake ...
- - Build the project: cmake --build ..
+1. Install CMake for building the project.
+2. Clone the repository: `git clone [repository-url]`.
+3. Navigate to the project directory: `cd [project-directory]`.
+4. Create and enter the build directory: `mkdir build && cd build`.
+5. Configure with CMake: `cmake ...`.
+6. Build the project: `cmake --build ..`.
 
 ### Usage
-
-First, ensure that the library is properly imported in your Python script:
-
-```
+Import the library in your Python script:
+```python
 import ipy_selfdual as ipy
 ```
-
-Then, you can use the run_optimization function as follows:
-
-```
-# Define your problem parameters
-A = ... # Coefficient matrix
-b = ... # Right-hand side vector
-c = ... # Cost vector
-lo = ... # Lower bounds for variables
-hi = ... # Upper bounds for variables
-sense = ... # Constraint sense
-tol = ... # Tolerance
-
-# Run the optimization
+Optimize using `run_optimization`:
+```python
+# Define problem parameters
+A, b, c = ... # Coefficient matrix, RHS vector, Cost vector
+lo, hi = ... # Variable bounds
+sense, tol = ... # Constraint sense, Tolerance
+
+# Execute optimization
 x0, lambdas, slacks, obj = ipy.run_optimization(A, b, -c, lo, hi, sense_ipm, tol)
 
-# x0: Solution vector
-# lambdas: Dual variables
-# slacks: Slack variables
-# obj: Objective
+# Outputs: Solution vector, Dual variables, Slack variables, Objective value
 ```
 
 ### Contact
-
-For any queries or collaborations, please contact Laio Oriel Seman at laio@ieee.org.
+For inquiries or collaborations, reach out to Laio Oriel Seman at laio@ieee.org.