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Definition 1. A function f : S ⊂ Rn → R defined on a convex set S is concave if for any two points x1 x2 ∈ , S and for any λ ∈ [0, 1] we have: λx1 (1 − λ) x2 ≥ λf(x1) (1 − λ)f(x2) + +. is called strictly concave if for any two points x1 , x2 ∈ S and for any λ ∈ (0, 1) we have: λx1 (1 − λ) x2 > λf(x1) (1 − λ)f(x2) + +.
Feb 1, 2017 · I have the following code below that prints the PDF graph for a particular mean and standard deviation. Now I need to find the actual probability, of a particular value. So for example if my mean is 0, and my value is 0, my probability is 1.
- a r i e s t h e angle , # t h e second v a r i e s t h e c i r c l e s
- a r i e s t h e angle , # t h e second v a r i e s t h e c i r c l e s
- a r i e s t h e angle , # t h e second v a r i e s t h e c i r c l e s
- a r i e s t h e angle , # t h e second v a r i e s t h e c i r c l e s
line = x [ na , : ] + r [ na , : ] np . s i n ( ∗ h i [ : , na ] ) line = y [ na , : ] + r [ na , : ] np . cos ( h i [ : , na ] ∗ ) ax= p l t . p l o t ( x line , y line , ’− ’ )
line = x [ na , : ] + r [ na , : ] ∗ np . s i n ( h i [ : , na ] ) line = y [ na , : ] + r [ na , : ] np . cos ( h i [ : , na ] ) ∗ ax= p l t . p l o t ( x line , y line , ’− ’ )
line = x [ na , : ] + r [ na , : ] ∗ np . s i n ( h i [ : , na ] ) line = y [ na , : ] + r [ na , : ] np . cos ( h i [ : , na ] ) ∗ ax= p l t . p l o t ( x line , y line , ’− ’ )
line = x [ na , : ] + r [ na , : ] np . s i n ( h i [ : , na ] ) ∗ line = y [ na , : ] + r [ na , : ] np . cos ( ∗ h i [ : , na ] ) ax= p l t . p l o t ( x line , y line , ’− ’ )
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Anatomy of a Function def main(): mid = average(10.6, 7.2) print(mid) def average(a, b): sum = a + b return sum / 2 Think/Pair/Share: Find the function definition, function name, parameter(s), and return value in average.
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function cvx_optval = g(y) cvx_begin variable t; maximize(t) subject to pos(t) + pow_pos(t, 1.5) + pow_pos(t, 2.5) <= y; cvx_end. use it as an ordinary function, as in g(14.3), or within CVX as a concave function: cvx_begin variables x y; minimize(quad_over_lin(x, y) + 4*x + 5*y) subject to g(x) + 2*g(y) >= 2; cvx_end.
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It is also possible to characterize concavity or convexity of functions in terms of the convexity of particular sets. Given the graph of a function, the hypograph of f,
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The analysis of quadratic functions from Chapter 1 becomes a fundamental tool for describing behavior that is beyond the linear approximation, such as bending (convexity/concavity).
