🌍 Week 6 Homework — Feedback

Student: Michele Nascia
Assignment: Solow Model Calibration: Grid Search vs Optimization Tools

✅ Overall Assessment

Result: ✅ More than 50% Correct

Excellent submission with all three optimization methods correctly implemented. The objective plot correctly shows all three optima with distinct markers, and the model fit plot shows all three methods for comparison. Comparison comments are provided. However, timing measurements are missing for all three methods. The code structure is good with clear documentation.

🔍 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, ub=1)
5.2 Call fmincon with proper syntax ✅ fmincon correctly called with proper options
6.1 Display computation times ❌ Missing: No timing measurements (tic/toc) for any method
6.2 Display optimization results ✅ Displays results for all three methods using table format
6.3 Comment comparing methods ✅ Provides comparison comments (lines 97-100) 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 ✅ Figures correctly saved using saveas() and savefig()

📈 Technical Implementation

  • Grid Search: Correctly implemented with proper loop and minimum finding
  • fminsearch with Sigmoid: Properly reparameterized using sigmoid function
  • fmincon with Bounds: Correctly implemented with proper options
  • Helper Function: solow_simulate() correctly implements Solow dynamics (separate file)
  • Timing: ❌ Missing - No timing measurements for any method
  • Figure Management: Creates Figures directory and saves figures properly using saveas() and savefig()
  • Output Format: Uses table format for displaying results (excellent presentation)

💬 Style & Clarity

  • Code Quality: Good organization with clear section headers
  • Variable Naming: Clear and descriptive (s_hat_grid, s_hat_nelder, s_hat_con)
  • Comments: Good documentation with section labels
  • Output: Uses fprintf and table format for displaying results (excellent presentation)
  • 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 (black circle), fminsearch (red square), fmincon (blue diamond) with distinct markers
  • Styling: Good styling with proper labels, legend, grid
  • Saving: ✅ Saves to Figures/ directory in both PNG and FIG formats
  • Quality: Excellent - clearly distinguishes all three methods

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
  • Styling: Appropriate styling with proper labels, legend, grid
  • Saving: ✅ Saves to Figures/ directory in both PNG and FIG formats
  • Quality: Excellent visualization comparing all three methods

✅ Suggestions for Improvement

  1. CRITICAL: Add timing measurements for all three methods: 
    tic;
% ... grid search code ...
time_grid = toc;
   
tic;
% ... fminsearch code ...
time_fminsearch = toc;
   
tic;
% ... fmincon code ...
time_fmincon = toc;
   
fprintf('Time (Grid search): %.4f seconds\n', time_grid);
fprintf('Time (fminsearch): %.4f seconds\n', time_fminsearch);
fprintf('Time (fmincon): %.4f seconds\n', time_fmincon);

🎯 Summary

Excellent submission with one missing requirement. The student demonstrates strong understanding of optimization methods, implementing all three methods correctly (grid search, fminsearch with sigmoid, and fmincon). The code includes good organization with clear sections, comparison comments discussing speed, robustness, and similarity, excellent model fit plot showing all three methods, and excellent output formatting using table. However, one issue is present: no timing measurements for any method. Figures are properly saved in multiple formats.

Grade Level: ✅ More than 50% Correct (11/12 tasks fully correct, 0/12 partially correct, 1/12 incorrect)