Convexity意思
"Convexity" is a mathematical term that has several meanings depending on the context. Here are some common definitions:
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In geometry: A convex set is a set for which every pair of points can be connected by a line segment that lies entirely within the set. A convex function is a function whose epigraph (the set of points on and above the graph in the plane) is a convex set.
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In finance and economics: Convexity is a measure of the curvature of the relationship between the rate of return on an investment and changes in interest rates. It is used to describe the shape of the yield curve or the sensitivity of the price of a bond to changes in interest rates.
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In optimization: Convex optimization problems are those where the objective function and the constraints are all convex. This property makes these problems particularly well-behaved, as they have unique solutions and efficient algorithms for finding them.
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In physics: Convexity can refer to the property of a lens or mirror that causes light to bend toward the normal (converging).
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In statistics: Convexity is a measure of the shape of a probability distribution. It is used to describe the degree to which a distribution is peaked or flat.
The meaning of "convexity" can vary depending on the field of study, but in all cases, it refers to a property that is related to the concept of being curved outward or having a shape that is similar to the shape of a half-circle.