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An example of mildly elevated ST segments in V1 to V3 that are concave down An ST elevation is considered significant if the vertical distance inside the ECG trace and the baseline at a point 0.04 seconds after the J-point is at least 0.1 mV (usually representing 1 mm or 1 small square) in a limb lead or 0.2 mV (2 mm or 2 small squares) in a ...
This function is quasiconcave, but it is not concave (in fact, it is strictly convex). It can be concavified, for example, using the monotone transformation () = /, since (()) = is concave. Not every concave function can be concavified in this way. A counter example was shown by Fenchel. [2]
The term convex is often referred to as convex down or concave upward, and the term concave is often referred as concave down or convex upward. [ 3 ] [ 4 ] [ 5 ] If the term "convex" is used without an "up" or "down" keyword, then it refers strictly to a cup shaped graph ∪ {\displaystyle \cup } .
The following are among the properties of log-concave distributions: If a density is log-concave, so is its cumulative distribution function (CDF). If a multivariate density is log-concave, so is the marginal density over any subset of variables. The sum of two independent log-concave random variables is log-concave. This follows from the fact ...
A function f is concave over a convex set if and only if the function −f is a convex function over the set. The sum of two concave functions is itself concave and so is the pointwise minimum of two concave functions, i.e. the set of concave functions on a given domain form a semifield.
The epigraph of f is a convex set if and only if f is a convex function. The following theorems present some functions f for which the epigraph has an SCB. Let g(t) be a 3-times continuously-differentiable concave function on t>0, such that | ‴ | / | ″ | is bounded by a constant (denoted 3*b) for all t>0.
Convex optimization is a subfield of mathematical optimization that studies the problem of minimizing convex functions over convex sets (or, equivalently, maximizing concave functions over convex sets). Many classes of convex optimization problems admit polynomial-time algorithms, [1] whereas mathematical optimization is in general NP-hard. [2 ...
Consider a family of convex optimization problems of the form: minimize f(x) s.t. x is in G, where f is a convex function and G is a convex set (a subset of an Euclidean space R n). Each problem p in the family is represented by a data-vector Data( p ), e.g., the real-valued coefficients in matrices and vectors representing the function f and ...