This article summarizes the basic ideas of convex optimization in finite-dimensional vector spaces. Duality, the Fenchel transforms and the subdifferential are introduced and used to discuss Lagrangean duality and the Kuhn–Tucker theorem. Applications of these ideas can be found in duality.
KeywordsConcave optimization Conjugate duality th Convex optimization Convex programming Convexity Duality Fenchel transform Hyperplanes Kuhn–Tucker th Lagrange multipliers Monotonicity Quasi-concavity Saddlepoints Separation th
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