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Concave function - Wikipedia, the free encyclopedia
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is said to be concave on an interval [a,b] if, for any points x_1 and x_2 in [a,b] , the function -f(x) is convex on that interval (Gradshteyn and Ryzhik ...
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A function f(x) is logarithmically concave on the interval [a,b] if f>0 and lnf(x) ... Weisstein, Eric W. "Logarithmically Concave Function. ...
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The next example shows that a nondecreasing concave transformation of a concave function is concave. ... Example Let U be a concave function and g a nondecreasing and concave function. Define the function f by f (x) = g(U(x)) for all x. Show that f is concave.
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A function f(·) is concave if, for any positive weights w1 and w2 such that w1 + w2 = 1, then ... Arbitrage Pricing; Arbitrage Profit; Average Cost; Balance of Payments; Budget Constraint; Call Option; Concave Function; Consumer Surplus; Consumption Function; Convex Function; Deadweight Loss; Demand Curve;
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Logarithmically concave function - Wikipedia, the free encyclopedia
A function f : \R^n \to \R^+ is logarithmically concave (or log-concave for short), if its natural logarithm \ln(f(x)) , is concave. Note that we allow here concave functions to take value -\...
en.wikipedia.org/wiki/Logarithmically_concave_function |
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Verify that the epigraph is a convex set and so the function is convex. You may wish to rotate the plot to see this. Also verify that the function g = -f is a concave function.
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A sufficient condition for a saddle point to exist is that X and Y are non-empty, compact, convex sets, f(.,y) is convex on X for each y in Y, and f(x,.) is concave on Y for each x in X. Saddle point equivalence underlies duality. ... Strictly concave function. Negative is strictly convex.
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A function f(x) is concave if -f(x) is convex. Equivalently, the line connecting two points on the graph lies below the graph. In symbols, reverse the direction of the inequality for convexity. ... The running average of a log concave function is also log concave.
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J.A. Calvin and R.L. Dykstra. A note on maximizing a special concave function subject to simultaneous loewner order constraints. Linear Algebra and Its Applications 176, pages 37--44, 1992. ... A note on maximizing a special concave function subject to simultaneous Lowner order constraints. Linear Algebra Appl., 176:37--44,
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