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[37] | 1 | function YESNONA = isconvex(p) |
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| 2 | %ISCONVEX Checks if scalar function is convex |
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| 3 | |
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| 4 | % Author Johan Löfberg |
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| 5 | % $Id: isconvex.m,v 1.2 2005/10/05 20:50:42 joloef Exp $ |
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| 6 | p=p; |
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| 7 | if is(p,'linear') |
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| 8 | YESNONA = 1; |
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| 9 | return; |
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| 10 | elseif is(p,'quadratic') |
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| 11 | [Q,c,f,x,info] = quaddecomp(p); |
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| 12 | if ~info |
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| 13 | if all(real(eig(Q+Q')) > -1e-13) |
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| 14 | YESNONA = 1; |
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| 15 | end |
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| 16 | end |
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| 17 | end |
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| 18 | |
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| 19 | vars = depends(p); |
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| 20 | x = recover(depends(p)); |
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| 21 | convex = 1; |
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| 22 | iterations = 0; |
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| 23 | while convex & iterations<10 |
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| 24 | y1 = randn(length(vars),1); |
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| 25 | assign(x,y1); |
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| 26 | p1 = double(p); |
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| 27 | y2 = randn(length(vars),1); |
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| 28 | assign(x,y2); |
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| 29 | p2 = double(p); |
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| 30 | yc = ((y1+y2)/2); |
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| 31 | assign(x,yc); |
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| 32 | pc = double(p); |
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| 33 | if pc>(p1+p2)/2 |
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| 34 | convex = 0; |
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| 35 | end |
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| 36 | iterations = iterations + 1; |
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| 37 | end |
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| 38 | |
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| 39 | % Maybe we didn't manage to prove non-convexity |
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| 40 | if convex |
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| 41 | H = hessian(p,x); |
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| 42 | v = sdpvar(length(H),1); |
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| 43 | sol = solvesos(set(sos(v'*H*v)),[],sdpsettings('verbose',1)); |
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| 44 | if sol.problem == 0 |
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| 45 | YESNONA = 1; |
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| 46 | else |
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| 47 | YESNONA = nan; |
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| 48 | end |
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| 49 | else |
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| 50 | YESNONA = 0; |
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| 51 | end |
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| 52 | |
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