Strictly convex information

Strictly convex may refer to: Strictly convex function, a function having the line between any two points above its graph Strictly convex polygon, a polygon...

Strongly convex functions are in general easier to work with than convex or strictly convex functions, since they are a smaller class. Like strictly convex functions...

polygon is convex if every line that does not contain any edge intersects the polygon in at most two points. A strictly convex polygon is a convex polygon...

closed convex subset is strictly convex if and only if every one of its boundary points is an extreme point. A set C is absolutely convex if it is convex and...

strictly convex space is a normed vector space (X, || ||) for which the closed unit ball is a strictly convex set. Put another way, a strictly convex...

deltahedron has an even number of faces. Only eight deltahedra are strictly convex; these have 4, 6, 8, 10, 12, 14, 16, or 20 faces. These eight deltahedra...

include the closed convex curves (the boundaries of bounded convex sets), the smooth curves that are convex, and the strictly convex curves, which have...

\}}} A (strictly) quasiconvex function has (strictly) convex lower contour sets, while a (strictly) quasiconcave function has (strictly) convex upper contour...

x_{n}\}}.} The LogSumExp function is convex, and is strictly increasing everywhere in its domain (but not strictly convex everywhere). Writing x = ( x 1 ,...

said to be strictly less than an element b, if a ≤ b and a ≠ b . {\displaystyle a\neq b.} For example, { x } {\displaystyle \{x\}} is strictly less than...

a\}} are convex sets. A differentiable function f is (strictly) concave on an interval if and only if its derivative function f ′ is (strictly) monotonically...

{\displaystyle {\log }\circ f} is convex, and Strictly logarithmically convex if log ∘ f {\displaystyle {\log }\circ f} is strictly convex. Here we interpret log...

Convex optimization is a subfield of mathematical optimization that studies the problem of minimizing convex functions over convex sets (or, equivalently...

relation is convex, but not strictly-convex. 3. A preference relation represented by linear utility functions is convex, but not strictly convex. Whenever...

Duality: If F is strictly convex, then the function F has a convex conjugate F ∗ {\displaystyle F^{*}} which is also strictly convex and continuously...

strictly convex function of the two points, unlike the distance, which is non-smooth (near pairs of equal points) and convex but not strictly convex....

{\displaystyle M} is positive definite if and only if its quadratic form is a strictly convex function. More generally, any quadratic function from R n {\displaystyle...

a strictly convex drawing, for instance obtained as the Schlegel diagram of a convex polyhedron representing the graph. For these graphs, a convex (but...

functions (coercive functions). The 2-norm and ∞-norm are strictly convex, and thus (by convex optimization) the minimizer is unique (if it exists), and...

In geometry, a Johnson solid is a strictly convex polyhedron each face of which is a regular polygon. There is no requirement that each face must be the...

consumer has strictly convex preferences, then the Marshallian demand is unique and continuous. In contrast, if the preferences are not convex, then the...

augmented to a central cube. This is a failed Johnson solid for not being strictly convex. This is also a space-filling polyhedron, and matches the geometry...

≤) is replaced by the strict inequality then f {\displaystyle f} is called strictly convex. Convex functions are related to convex sets. Specifically, the...

f(t)} is convex, so is A ↦ Tr ⁡ f ( A ) {\displaystyle A\mapsto \operatorname {Tr} f(A)} on Hn, and it is strictly convex if f is strictly convex. See proof...

construction of a strictly convex compact surface S whose Gaussian curvature is specified. More precisely, the input to the problem is a strictly positive real...

\end{cases}}} The convex conjugate and Legendre transform of the exponential function agree except that the domain of the convex conjugate is strictly larger as...

requirement. If the normed space is Euclidean, or, more generally, strictly convex, then ‖ x + y ‖ = ‖ x ‖ + ‖ y ‖ {\displaystyle \|x+y\|=\|x\|+\|y\|}...