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The 22 pages that link to Convex function, each with the reason it gives.

• Gradient descentRelated: Convexity gives stronger guarantees about minima and convergence.

• Convex optimizationBroader topic: Convex objectives ensure local minima are global.

• Jensen's inequalityNarrower topic: Its defining property supplies Jensen’s inequality for weighted averages.

• Objective functionRelated: Convexity can make local minima of an objective global minima.

• ConvexityBroader topic: This is the functional version of convexity, defined by an inequality.

• Monotonic functionCompared with: Convexity constrains curvature, not consistent increase or decrease.

• Legendre transformRelated: Convexity ensures the slope identifies a supporting tangent and helps recover the original function.

• Convex analysisBroader topic: Convex functions have tractable minima and support much of convex optimization.

• Monotone functionCompared with: Convexity constrains averages and curvature rather than ordered pairs.

• Positive-definite matrixRelated: A positive-definite Hessian throughout a convex domain makes a twice-differentiable function strictly convex.

• MajorizationRelated: Convexity makes averaging reduce summed function values, as majorization predicts.

• Bernoulli's inequalityRelated: For exponents at least one, convexity places the power curve above its tangent at one.

• Hadamard three-circle theoremRelated: Convexity applies to the maximum-modulus profile against log-radius.

• Numerical optimizationRelated: Convexity can make local minima global and provide strong guarantees for algorithms.

• Cartan–Hadamard theoremRelated: Geodesic convexity is especially well behaved on Hadamard manifolds.

• Hermite–Hadamard inequalityNarrower topic: The inequality follows from this defining chord property.

• Karamata's inequalityNarrower topic: Convexity makes greater spread increase the sum of function values.

• Muirhead's inequalityRelated: Convexity underlies the averaging principle behind majorization inequalities.

• Young's inequality for productsNarrower topic: Convexity underlies both the power-function proof and the Fenchel–Young generalization.

• Bohr–Mollerup theoremNarrower topic: Log-convexity is ordinary convexity applied after taking a logarithm.

• Gibbs' inequalityNarrower topic: Convexity underlies the inequalities used to establish nonnegative divergence.

• Levinson's inequalityNarrower topic: Nonnegative third derivative makes the first derivative convex, enabling the paired-sum comparison.