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"Optimality conditions" is a cross-disciplinary book category focused on the mathematical criteria and principles that determine when a solution is best according to a given objective and constraints. Titles in this category treat necessary and sufficient conditions for optimality—from first- and second-order conditions and convexity arguments to Karush–Kuhn–Tucker theory, Lagrange multipliers, duality, variational inequalities, and Pontryagin’s maximum principle—alongside existence, uniqueness, and sensitivity analyses. Works range from rigorous theoretical texts with proofs and general frameworks to applied guides showing how to derive and verify optimality conditions in economics, control theory, machine learning, engineering design, and numerical optimization, often including worked examples and computational techniques for checking and exploiting these conditions.

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