51 lines
973 B
Mathematica
51 lines
973 B
Mathematica
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function YESNONA = isconvex(p)
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%ISCONVEX Checks if scalar function is convex
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p=p;
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if is(p,'linear')
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YESNONA = 1;
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return;
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elseif is(p,'quadratic')
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[Q,c,f,x,info] = quaddecomp(p);
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if ~info
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if all(real(eig(Q+Q')) > -1e-13)
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YESNONA = 1;
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end
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end
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end
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vars = depends(p);
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x = recover(depends(p));
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convex = 1;
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iterations = 0;
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while convex & iterations<10
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y1 = randn(length(vars),1);
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assign(x,y1);
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p1 = double(p);
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y2 = randn(length(vars),1);
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assign(x,y2);
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p2 = double(p);
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yc = ((y1+y2)/2);
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assign(x,yc);
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pc = double(p);
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if pc>(p1+p2)/2
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convex = 0;
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end
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iterations = iterations + 1;
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end
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% Maybe we didn't manage to prove non-convexity
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if convex
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H = hessian(p,x);
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v = sdpvar(length(H),1);
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sol = solvesos((sos(v'*H*v)),[],sdpsettings('verbose',1));
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if sol.problem == 0
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YESNONA = 1;
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else
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YESNONA = nan;
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end
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else
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YESNONA = 0;
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end
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