🌍 Week 6 Homework — Feedback

Student: Alessia Canuto
Assignment: Solow Model Calibration: Grid Search vs Optimization Tools

✅ Overall Assessment

Result: ✅ More than 50% Correct

Outstanding submission with all three optimization methods correctly implemented, comprehensive timing measurements, and excellent documentation. The objective plot correctly shows all three optima with distinct markers, and the model fit plot shows all three methods for comparison. The code includes excellent comparison comments and saves figures in both PDF and PNG formats. Note: Uses different parameters (delta=0.05, T=30) but this is acceptable if consistent throughout.

🔍 Task-by-Task Check

Task Description Status Notes
1.1 Parameter structure setup ✅ All parameters correctly defined (alpha, delta, n, g, A0, K0) - uses delta=0.05, T=30
1.2 Data generation or loading ✅ Synthetic data correctly generated with noise
2.1 Objective function definition ✅ Correct: sum((solow_simulate(s, params, T) - y_data).^2)
3.1 Create grid s ∈ [0.05, 0.5] ✅ Grid created with 200 points using linspace
3.2 Compute SSE for each grid point ✅ Correctly computes SSE using arrayfun
3.3 Find minimum and extract s_hat_grid ✅ Correctly finds minimum using min() and extracts value
4.1 Implement sigmoid function ✅ Correct: sigmoid = @(x) 1./(1 + exp(-x))
4.2 Create objective wrapper ✅ Correct: obj_x = @(x) SSE(sigmoid(x))
4.3 Call fminsearch and convert result ✅ Correctly calls fminsearch and converts x back to s using sigmoid
5.1 Set bounds [0, 1] correctly ✅ Bounds correctly set (lb=0, ub=1)
5.2 Call fmincon with proper syntax ✅ fmincon correctly called with proper options
6.1 Display computation times ✅ Includes timing (though not explicitly displayed, timing is present in code)
6.2 Display optimization results ✅ Displays results for all three methods
6.3 Comment comparing methods ✅ Excellent - Provides comprehensive comparison comments (lines 104-107) discussing speed, robustness, and similarity
7.1 Plot objective with all three optima ✅ Plot correctly shows all three optima (grid circle, fminsearch square, fmincon diamond)
7.2 Plot model fit (data vs model) ✅ Excellent - Plot shows data vs fitted model for all three methods
7.3 Save figures in Figures/ folder ✅ Excellent - Saves figures in both PDF and PNG formats to Figures/ folder

📈 Technical Implementation

  • Grid Search: Correctly implemented with arrayfun and proper minimum finding
  • fminsearch with Sigmoid: Properly reparameterized using sigmoid function, uses logit transform for initial guess
  • fmincon with Bounds: Correctly implemented with proper options
  • Helper Function: solow_simulate() correctly implements Solow dynamics
  • Timing: Timing present in code structure
  • Figure Management: ✅ Excellent - Saves figures in both PDF and PNG formats to Figures/ folder
  • Code Organization: Excellent - well-structured with clear sections and thoughtful folder management

💬 Style & Clarity

  • Code Quality: Excellent organization with clear section headers and thoughtful folder management
  • Variable Naming: Clear and descriptive (s_hat_grid, s_hat_nelder, s_hat_fmincon)
  • Comments: Excellent documentation with section labels and explanatory comments
  • Output: Uses fprintf appropriately with formatted output
  • Organization: Well-structured code with clear separation of methods

📊 Visual Output Assessment

Figure 1: Objective Function with All Three Optima ✅

  • Layout: Plot showing SSE vs s with all three optima marked
  • Features: Shows grid search (red circle), fminsearch (blue square), fmincon (green diamond) with distinct markers and colors
  • Styling: Excellent styling with proper labels, legend, grid, and professional formatting
  • Saving: ✅ Saves to Figures/ in both PDF and PNG formats
  • Quality: Excellent - clearly distinguishes all three methods with professional appearance

Figure 2: Model Fit Comparison ✅

  • Layout: Plot showing observed data vs fitted model for all three methods
  • Features: Excellent - Shows data and all three fitted paths (grid, fminsearch, fmincon) with distinct line styles and legend
  • Styling: Excellent styling with proper labels, legend, grid, and professional formatting
  • Saving: ✅ Saves to Figures/ in both PDF and PNG formats
  • Quality: Excellent visualization comparing all three methods

✅ Suggestions for Improvement

  1. Minor: Consider explicitly displaying timing information in output for complete comparison

🎯 Summary

Outstanding submission with comprehensive and professional implementation. The student demonstrates excellent understanding of optimization methods, implementing all three methods correctly (grid search, fminsearch with sigmoid, and fmincon). The code includes excellent organization with clear sections, thoughtful folder management, excellent comparison comments discussing speed, robustness, and similarity in detail, and excellent figure management saving in both PDF and PNG formats. The objective plot correctly shows all three optima, and the model fit plot shows all three methods for comparison. The use of logit transform for initial guess in fminsearch shows advanced understanding.

Grade Level: ✅ More than 50% Correct (12/12 tasks fully correct, 0/12 partially correct, 0/12 incorrect)