🌍 Week 6 Homework — Feedback

Student: Iusupova Farangizbegim
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 and clear code organization. The objective plot correctly shows all three optima with distinct markers, and comprehensive comparison comments are provided. However, one required element is missing: No timing measurements (tic/toc) for comparing computation speeds. The code structure is clear with good documentation and proper figure management.

🔍 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 with noise 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 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
5.1 Set bounds [0, 1] correctly ✅ Bounds set to [0.001, 0.999] (acceptable, slightly tighter)
5.2 Call fmincon with proper syntax ✅ fmincon correctly called with proper syntax and options
6.1 Display computation times ❌ Missing: No tic/toc measurements for any method
6.2 Display optimization results ✅ Excellent - displays comprehensive summary table with all methods
6.3 Comment comparing methods ✅ Excellent - Provides detailed comparison comments (lines 134-141) discussing speed, robustness, and similarity
7.1 Plot objective with all three optima ✅ Plot correctly shows all three optima (grid red circle, fminsearch blue square, fmincon green diamond)
7.2 Plot model fit (data vs model) ✅ Correct plot showing data vs fitted model output over time
7.3 Save figures in Figures/ folder ✅ Figures correctly saved in PNG format

📈 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
  • Figure Management: Creates Figures directory and saves figures properly
  • Output Formatting: Excellent - uses fprintf with formatted summary table
  • Code Organization: Well-structured with clear sections and labeled steps

💬 Style & Clarity

  • Code Quality: Excellent 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 appropriately with formatted table output
  • Organization: Well-structured code matching homework requirements
  • Documentation: Clear comments explaining each section

📊 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
  • Styling: Good styling with proper labels, legend, grid, and custom axis settings
  • Saving: ✅ Saves to Figures/ directory
  • Quality: Excellent - clearly distinguishes all three methods

Figure 2: Model Fit ✅

  • Layout: Plot showing observed data vs fitted model output over time
  • Features: Shows data (black circles) and fitted model (red dashed line) with proper legend
  • Styling: Appropriate styling with proper labels, legend, and grid
  • Saving: ✅ Saves to Figures/ directory
  • Quality: Good visualization of model fit

✅ Suggestions for Improvement

  1. CRITICAL: Add timing measurements (tic/toc) 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 minor missing requirements. The student demonstrates strong 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 comparison comments discussing speed, robustness, and similarity of results, and proper figure management showing all three optima clearly. However, one required element is missing: no timing measurements for comparing computation speeds. The code structure is excellent with clear documentation and formatted output.

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