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Add Augmented Lagrangian and SQP Methods - #1

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Add Augmented Lagrangian and SQP Methods#1
GinyuSpecialForce wants to merge 4 commits into
prasanna00019:mainfrom
GinyuSpecialForce:main

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Summary

This PR adds two important constrained optimization methods to the repository:

New Methods:

  1. Augmented Lagrangian Method (ALM)

    • Handles both equality and inequality constraints
    • Includes structural engineering application example
    • Visual convergence plots
    • Full implementation with BFGS updates
  2. Sequential Quadratic Programming (SQP)

    • State-of-the-art constrained optimization
    • Faster convergence than penalty methods
    • Includes Rosenbrock function example
    • BFGS Hessian updates

Files Added:

  • Augmented_Lagrangian_Method.ipynb
  • SQP_Method.ipynb

Examples Include:

  • Simple constrained problems (equality/inequality)
  • Structural optimization application
  • Rosenbrock function with circle constraint
  • Convergence visualization

These methods fill a gap in the repository for nonlinear constrained optimization (currently only linear Simplex is available).

This notebook introduces the Augmented Lagrangian Method for solving constrained nonlinear optimization problems, detailing its mathematical formulation, algorithm steps, and advantages over penalty methods. It includes examples of constrained optimization problems and their solutions using the method.
This notebook introduces the Sequential Quadratic Programming (SQP) method for constrained optimization, detailing its mathematical formulation, advantages, and algorithm steps. It includes an implementation example using the Rosenbrock function with constraints.
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