Merge pull request #78 from LearningToOptimize/class02-overview-update

Class 2: update overview.md

Author: andrewrosemberg

class02/overview.md

@@ -4,39 +4,20 @@
 
 **Topic:** Numerical optimization for control (gradient/SQP/QP); ALM vs. interior-point vs. penalty methods
 
-**Pluto Notebook for all the chapter**: Here is the actual [final chapter](https://learningtooptimize.github.io/LearningToControlClass/dev/class02/class02.html)
-
 ---
 
 ## Overview
 
 This class covers the fundamental numerical optimization techniques essential for optimal control problems. We explore gradient-based methods, Sequential Quadratic Programming (SQP), and various approaches to handling constraints including Augmented Lagrangian Methods (ALM), interior-point methods, and penalty methods.
 
-## Learning Objectives
-
-By the end of this class, students will be able to:
-
-- Understand the mathematical foundations of gradient-based optimization
-- Implement Newton's method for unconstrained minimization
-- Apply root-finding techniques for implicit integration schemes
-- Solve equality-constrained optimization problems using Lagrange multipliers
-- Compare and contrast different constraint handling methods (ALM, interior-point, penalty)
-- Implement Sequential Quadratic Programming (SQP) for nonlinear optimization
-
-## Prerequisites
 
-- Solid understanding of linear algebra and calculus
-- Familiarity with Julia programming
-- Basic knowledge of differential equations
-- Understanding of optimization concepts from Class 1
+The slides for this lecture can be found here [Lecture Slides (PDF)](https://learningtooptimize.github.io/LearningToControlClass/dev/class02/ISYE_8803___Lecture_2___Slides.pdf)
 
-## Materials
-
-### Interactive Notebooks
-
-The class is structured around four interactive Jupyter notebooks that build upon each other:
+The Pluto julia notebook for my final chapter can be found here [final chapter](https://learningtooptimize.github.io/LearningToControlClass/dev/class02/class02.html) 
 
+Although the main code for the julia demo's are contained in the Pluto notebook above, the following julia notebooks are the demo's I used in the class recording/presentation.
 
+ 
 1. **[Part 1a: Root Finding & Backward Euler](https://learningtooptimize.github.io/LearningToControlClass/dev/class02/part1_root_finding.html)**
    - Root-finding algorithms for implicit integration
    - Fixed-point iteration vs. Newton's method
@@ -48,49 +29,18 @@ The class is structured around four interactive Jupyter notebooks that build upo
    - Unconstrained optimization fundamentals
    - Newton's method for minimization
    - Hessian matrix and positive definiteness
-   - Regularization and line search techniques
-   - Practical implementation with Julia
+   - Regularization and line search techniques 
 
 3. **[Part 2: Equality Constraints](https://learningtooptimize.github.io/LearningToControlClass/dev/class02/part2_eq_constraints.html)**
    - Lagrange multiplier theory
    - KKT conditions for equality constraints
-   - Quadratic programming with equality constraints
-   - Visualization of constrained optimization landscapes
-   - Practical implementation examples
+   - Quadratic programming with equality constraints 
 
 4. **[Part 3: Interior-Point Methods](https://learningtooptimize.github.io/LearningToControlClass/dev/class02/part3_ipm.html)**
    - Inequality constraint handling
    - Barrier methods and log-barrier functions
-   - Interior-point algorithm implementation
-   - Comparison with penalty methods
-   - Convergence properties and practical considerations
-
-### Additional Resources
-
-- **[Lecture Slides (PDF)](https://learningtooptimize.github.io/LearningToControlClass/dev/class02/ISYE_8803___Lecture_2___Slides.pdf)** - Complete slide deck from the presentation 
-- **[Demo Script](https://learningtooptimize.github.io/LearningToControlClass/dev/class02/penalty_barrier_demo.py)** - Python demonstration of penalty vs. barrier methods
-
-## Key Concepts Covered
-
-### Mathematical Foundations
-- **Gradient and Hessian**: Understanding first and second derivatives in optimization
-- **Newton's Method**: Quadratic convergence and implementation details
-- **KKT Conditions**: Necessary and sufficient conditions for optimality
-- **Duality Theory**: Lagrange multipliers and dual problems
-
-### Numerical Methods
-- **Root Finding**: Fixed-point iteration, Newton-Raphson method
-- **Implicit Integration**: Backward Euler for stiff ODEs
-- **Sequential Quadratic Programming**: Local quadratic approximations
-- **Interior-Point Methods**: Barrier functions and path-following
-
-### Constraint Handling
-- **Equality Constraints**: Lagrange multipliers and null-space methods
-- **Inequality Constraints**: Active set methods and interior-point approaches
-- **Penalty Methods**: Quadratic and exact penalty functions
-- **Augmented Lagrangian**: Combining penalty and multiplier methods
-
-
+   - Interior-point algorithm implementation 
+  
 ---
 
 *For questions or clarifications, please reach out to Arnaud Deza at adeza3@gatech.edu*