KnowraConvex functionLinked fromLinked fromThe 22 pages that link to Convex function, each with the reason it gives.All 22Broader topic 3Related 10Narrower topic 7Compared with 2Gradient descentRelated: Convexity gives stronger guarantees about minima and convergence.Objective functionRelated: Convexity can make local minima of an objective global minima.Legendre transformRelated: Convexity ensures the slope identifies a supporting tangent and helps recover the original function.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.Muirhead's inequalityRelated: Convexity underlies the averaging principle behind majorization inequalities.