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May 15, 2019 · Open in MATLAB Online. It depends on how you want to define them. Here, I define them as points where the slope is -0.5: Theme. Copy. f = @ (x) 1- (x./sqrt (1+x.^2)); % Create Function. x = linspace (-10, 10); h = x (2)-x (1); % Step Interval. dfdx = gradient (f (x),h); % Derivative.
In the example at your link, with pwr=4, 2nd order conditions would not have helped you. Sargondjani on 18 Dec 2021. In my example you would actually converge to [0.5,0.5] from any symmetric initial guess. Such symmetric guesses are regular choices, so it happens more easily than you might expect.
Bounding Regions. Compute convex hull, alpha shape, or boundaries around points. Create regions defined by boundaries that enclose a set of points. The boundary function allows you to specify the tightness of the fit around the points, while the convhull and convhulln functions return the smallest convex boundary. alphaShape objects offer ...
Nov 19, 2015 · If a function is not convex, you can disprove convexity by finding a counterexample: Graph the function if 2d or 3d. Plot the value of the function applied to convex combinations of two random points and look for non-convex regions.
Sep 5, 2015 · Definition (Concavity/Convexity of a function). Let f: Rn → R. We say that f is concave if for all x, y ∈ Rn and for all λ ∈ [0, 1] we have f(λx + (1 − λ)y) ≥ λf(x) + (1 − λ)f(y). And a function is convex if − f is concave, or f(λx + (1 − λ)y) ≤ λf(x) + (1 − λ)f(y). Definition (Quasi-concave/Quasi-convex). Let f: Rn → R.
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) + +.
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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.
