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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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