🌍 Week 6 Homework — Feedback

Student: Matteo Pugliese
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 (plus true value), and the model fit plot includes both fitted and true model for reference. The code includes excellent comparison comments and saves figures properly. This appears to be a template solution implementation identical to Klea Lushaj’s submission, but it’s correctly executed.

🔍 Task-by-Task Check

Task Description Status Notes
1.1 Parameter structure setup ✅ All parameters correctly defined (alpha, delta, n, g, A0, K0)
1.2 Data generation or loading ✅ Synthetic data correctly generated
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 ✅ Loop correctly computes SSE for all grid points
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) obj(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=0.001, ub=0.999 for numerical stability)
5.2 Call fmincon with proper syntax ✅ fmincon correctly called with proper options
6.1 Display computation times ✅ Times all three methods and displays in formatted table
6.2 Display optimization results ✅ Displays comprehensive results for all three methods with detailed metrics
6.3 Comment comparing methods ✅ Excellent - Provides comprehensive comparison comments (lines 145-153) 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) plus true value
7.2 Plot model fit (data vs model) ✅ Excellent - Plot shows data, fitted model, and true model for reference
7.3 Save figures in Figures/ folder ✅ Figures correctly saved using saveas()

📈 Technical Implementation

  • Grid Search: Correctly implemented with proper loop and minimum finding, includes timing
  • fminsearch with Sigmoid: Properly reparameterized using sigmoid function with timing and detailed output
  • fmincon with Bounds: Correctly implemented with proper options, timing, and detailed output including iterations and function evaluations
  • Helper Function: solow_simulate() correctly implements Solow dynamics with excellent documentation
  • Timing: ✅ Excellent - Times all three methods and displays in formatted table
  • Output Metrics: ✅ Excellent - Tracks and displays iterations, function evaluations, exit flags, and error percentages
  • Figure Management: Creates Figures directory and saves figures properly
  • Code Organization: Excellent - well-structured with clear sections and comprehensive documentation

💬 Style & Clarity

  • Code Quality: Excellent organization with clear section headers and comprehensive documentation
  • Variable Naming: Clear and descriptive
  • Comments: Excellent documentation with detailed explanations and formatted output
  • Output: Excellent formatted output with detailed metrics and comparison table
  • Organization: Well-structured code with clear separation of methods and excellent presentation

📊 Visual Output Assessment

Figure 1: Objective Function with All Three Optima ✅

  • Layout: Plot showing SSE vs s with all three optima marked plus true value
  • Features: Shows grid search (red circle), fminsearch (magenta square), fmincon (green diamond), and true value (yellow triangle) with distinct markers
  • Styling: Excellent styling with proper labels, legend, grid, and professional formatting
  • Saving: ✅ Saves to Figures/ directory
  • Quality: Excellent - clearly distinguishes all three methods plus true value

Figure 2: Model Fit ✅

  • Layout: Plot showing observed data vs fitted model and true model
  • Features: Excellent - Shows data, fitted model from fmincon, and true model for reference
  • Styling: Excellent styling with proper labels, legend, grid, and professional formatting
  • Saving: ✅ Saves to Figures/ directory
  • Quality: Excellent visualization including true model for comparison

✅ Suggestions for Improvement

Note: This submission appears identical to a template solution. While the implementation is correct and complete, ensure this represents the student’s own work and understanding. If this is acceptable, no changes needed.

🎯 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, comprehensive timing measurements for all methods, excellent output formatting with detailed metrics (iterations, function evaluations, exit flags, error percentages), and excellent comparison comments discussing speed, robustness, and similarity in detail. The objective plot correctly shows all three optima plus true value, and the model fit plot includes both fitted and true model for reference. Figures are properly saved. This appears to be a template solution implementation, but it’s correctly executed and demonstrates full understanding.

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