MATLAB Optimizer Derivative Audit

Purpose

Validate analytic gradients, Hessians, and constraint Jacobians against numerical derivatives and confirm optimizer callback wiring is correct.

When to Use

• •Debugging matlab optimization functions and functions that call the solvers
• •KNITRO convergence failures or suspicious solutions
• •Suspected sign/index/scaling errors in derivative code
• •Pre-port validation before translating MATLAB solver logic

Workflow

1. •Locate optimization stack.

• •Find objective and constraint definitions.
• •Find KNITRO call sites and callback registration.

1. •Verify parameter plumbing.

• •Confirm variable ordering and shape assumptions.
• •Confirm scaling and bounds mapping.
• •Confirm any transformed parameterization is inverted correctly.

1. •Validate derivatives numerically.

• •Compute finite-difference gradient checks.
• •Compute Hessian checks (or Hessian-vector checks where appropriate).
• •Validate constraint Jacobian entries.

1. •Isolate mismatch sources.

• •Classify by sign errors, missing terms, index offsets, scaling issues.
• •Reproduce on minimal parameter vectors and test cases.

1. •Report and patch.

• •Provide mismatch table with absolute and relative errors.
• •Provide concrete patch suggestions tied to line-level logic.
• •Re-run checks after edits.

Required Checks

• •Objective gradient vs finite differences
• •Hessian symmetry and finite-difference consistency
• •Constraint Jacobian vs finite differences
• •Callback dimensions/order expected by KNITRO
• •Bounds and scaling consistency

Output Template

• •Functions audited: objective, constraints, callbacks
• •Check points: parameter vectors used
• •Derivative errors: max abs/rel by block
• •Likely causes: ranked root causes
• •Patch plan: file-level actions
• •Recheck: pass/fail after changes

Guardrails

• •Keep algorithm choice unchanged unless requested.
• •Treat "numerically close enough" with explicit tolerances.
• •Separate optional Julia-port notes from core derivative audit.

Test Guidance

• •Use multiple points, not just one nominal calibration.
• •Include edge-case points near bounds.
• •Persist a small reproducer test to prevent regression.