Mathematics · Constrained Optimization
The second-order condition for a MAXIMUM of the constrained optimization problem: maximize U = f(X1, X2, ..., Xn) subject to g(X1, X2, ..., Xn) = 0, using the bordered Hessian matrix H̄, requires the principal minors to satisfy:
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- 1|H̄2| > 0, |H̄3| < 0, ... (alternating starting positive)✓
- 2|H̄2| < 0, |H̄3| < 0, ... (all negative)
- 3|H̄2| 0, ... (alternating starting negative)
- 4|H̄2| > 0, |H̄3| > 0, ... (all positive)
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|H̄2| > 0, |H̄3| < 0, ... (alternating starting positive)
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