query: Mid-point convexity and convexity
positive_passages.docid: 16943
positive_passages.text: Midpoint-Convex and Continuous Implies Convex
negative_passages.docid: 9138
negative_passages.text: Projection of a point onto a simple convex polytope
negative_passages.docid: 25738
negative_passages.text: Jensen's Inequality implies convexity?
negative_passages.docid: 103045
negative_passages.text: Composition of Proximal Operators
negative_passages.docid: 30572
negative_passages.text: Intersection of nested closed bounded convex sets in Euclidean space
negative_passages.docid: 57514
negative_passages.text: The Minkowski sum of two convex sets is convex
negative_passages.docid: 151981
negative_passages.text: Tangent line of a convex function
negative_passages.docid: 101690
negative_passages.text: Is linear function convex or concave?
negative_passages.docid: 78229
negative_passages.text: Proving that the tangent to a convex function is always below the function
negative_passages.docid: 67313
negative_passages.text: Proving $\{(x_1, x_2) \in \mathbb{R}^2_{+} \mid x_1 x_2 \geq 1\}$ is convex
negative_passages.docid: 158399
negative_passages.text: Show that $\{(x_1,x_2):x_1x_2\geq4,x_1>0,x_2>0\}$ is a convex set
negative_passages.docid: 150609
negative_passages.text: Triangle Inequality of the Cartesian product with Max function
negative_passages.docid: 35857
negative_passages.text: Characterization of log-convexity
negative_passages.docid: 86305
negative_passages.text: A secant inequality for convex functions
negative_passages.docid: 25171
negative_passages.text: Why does a convex set have the same interior points as its closure?
negative_passages.docid: 28878
negative_passages.text: Convex function of independent vs. correlated random variables redux
negative_passages.docid: 74608
negative_passages.text: Convex function as supremum of countably many affine functions