Optimization: Local and Global Extrema Short Notes for GATE DA: Concepts, Formulas, Worked Examples & Practice

    Optimization: Local and Global Extrema short notes for GATE DA: 1 study cards covering concepts, formulas, shortcuts and exam traps, plus solved practice questions.

    The Extrema Problem-Solving Checklist

    Summary

    Master Algorithm for Unconstrained Extrema

    P1
    The Convexity Check
    Is convex? (Check if is Positive Semi-Definite everywhere).
    If YES: Any stationary point is the Global Minimum. Stop here.
    P2
    First-Order Conditions
    Compute . Solve to find all stationary points .
    P3
    Second-Order Conditions
    Compute . For each stationary point , evaluate and classify:
    (Positive Definite) Strict Local Minimum
    (Negative Definite) Strict Local Maximum
    Mixed eigenvalue signs Saddle Point
    Semi-Definite with zero eigenvalues Inconclusive
    P4
    Global Comparison (If non-convex)
    Evaluate at all confirmed local minima. The smallest value is the Global Minimum.
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    Optimization: Local and Global Extrema Short Notes for GATE DA: Concepts, Formulas, Worked Examples & Practice

    Optimization: Local and Global Extrema short notes for GATE DA: 1 study cards covering concepts, formulas, shortcuts and exam traps, plus solved practice ques

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