This file contains the values of the optimal dual multiplier \lambda^* of the cardinality constraint \sum_{i \in N} x_i \leq k (with k = 10) in the Perspective Relaxation of the Mean-Variance portfolio problem with min buy-in constranits (and, of course, cardinality constraint) for the instances distributed on the web site http://www.di.unipi.it/optimize/Data/MV.html This is used to compute the improved Approximate Projected Perspective Reformulation (AP$^2$R+) of the instances; the corresponding .lp files are also distributed on the web site. In order to apply the Perspective Reformulation (Relaxation), the nonseparable quadratic objective function of the MV problem has to be partly diagonalized; doing so changes the PR, and therefore the value of the optimal dual multiplier. This is why we report three values of \lambda^*, one for each of the "small" (s), "large" (l) and "intermediate" (c = convex combination of s and l with multipliers 0.5) diagonals also distributed on the web site. Note that in order to recover the original optimal value of the problem you have to add to the value you obtain from the AP$^2$R+ reformulation the constant + k * \lambda^* (with k = 10). s c l pard200_a -18.178200 -18.177400 -17.818300 pard200_b -16.338700 -16.282500 -16.163300 pard200_c -16.065900 -16.122300 -16.133500 pard200_d -18.053800 -18.237000 -18.750100 pard200_e -17.888600 -17.917200 -17.816100 pard200_f -17.457200 -17.687100 -17.828500 pard200_g -16.494600 -16.367700 -16.136300 pard200_h -16.968100 -17.117900 -17.325400 pard200_i -17.971000 -18.112800 -18.244800 pard200_j -15.472800 -15.349400 -15.263800 orl200-005-a -6.079260 -6.215160 -6.379850 orl200-005-b -5.462400 -5.508590 -5.312600 orl200-005-c -5.732440 -5.819690 -5.796970 orl200-005-d -5.850960 -6.064640 -6.300140 orl200-005-e -5.795820 -5.964200 -6.130400 orl200-005-f -6.337610 -6.532860 -6.733700 orl200-005-g -5.919140 -6.116730 -6.271920 orl200-005-h -5.080800 -5.354200 -5.705770 orl200-005-i -5.798090 -5.922520 -6.030580 orl200-005-j -5.596450 -5.860430 -6.173040 orl200-05-a -3.471420 -3.656280 -3.811000 orl200-05-b -4.105620 -4.314430 -4.520720 orl200-05-c -4.203520 -4.377050 -4.522650 orl200-05-d -4.406160 -4.471450 -4.522650 orl200-05-e -4.027220 -4.024360 -3.887010 orl200-05-f -4.064290 -4.271870 -4.465140 orl200-05-g -4.223460 -4.408150 -4.610610 orl200-05-h -4.215520 -4.416540 -4.659180 orl200-05-i -3.780040 -3.958590 -4.049930 orl200-05-j -4.234970 -4.386560 -4.511780 pard300_a -28.329400 -28.764700 -29.653900 pard300_b -27.395200 -27.394800 -27.035800 pard300_c -27.041900 -27.082000 -27.200300 pard300_d -27.819700 -28.105300 -28.525200 pard300_e -27.227000 -27.681900 -28.609200 pard300_f -26.020000 -25.789900 -25.350200 pard300_g -26.021600 -26.111800 -26.044600 pard300_h -25.669600 -25.863800 -25.974900 pard300_i -26.916000 -27.176600 -27.529400 pard300_j -28.972000 -29.234400 -29.918200 orl300_005_a -10.067900 -10.279300 -10.571400 orl300_005_b -9.026020 -9.288090 -9.542410 orl300_005_c -9.491680 -9.706140 -9.887220 orl300_005_d -8.568800 -8.758660 -8.937120 orl300_005_e -8.935380 -9.297510 -9.742740 orl300_005_f -8.596020 -9.025620 -9.576060 orl300_005_g -9.330800 -9.666680 -10.213800 orl300_005_h -8.376850 -8.611850 -8.949350 orl300_005_i -8.779260 -9.094530 -9.443640 orl300_005_j -8.998630 -9.258830 -9.412180 orl300_05_a -5.994090 -6.261480 -6.763060 orl300_05_b -6.207690 -6.515050 -6.901650 orl300_05_c -6.608610 -6.931740 -7.347320 orl300_05_d -6.568350 -6.793740 -7.037550 orl300_05_e -6.129580 -6.412160 -6.677830 orl300_05_f -6.055840 -6.445450 -6.966870 orl300_05_g -5.988980 -6.177920 -6.440960 orl300_05_h -6.324100 -6.683540 -7.182190 orl300_05_i -4.434810 -4.158780 -3.391360 orl300_05_j -6.740140 -6.937800 -7.125360 pard400_a -35.907800 -36.091800 -36.639100 pard400_b -36.558400 -37.348100 -38.219800 pard400_c -35.304900 -35.231700 -35.068400 pard400_d -34.481800 -35.072900 -35.604500 pard400_e -36.254400 -36.445500 -36.413400 pard400_f -33.479900 -33.399400 -32.859800 pard400_g -37.554700 -37.905500 -38.664600 pard400_h -35.889800 -36.660800 -37.923900 pard400_i -36.681200 -37.212100 -37.839100 pard400_j -35.253700 -36.127500 -37.129600 orl400_005_a -12.495700 -12.783500 -13.092900 orl400_005_b -11.402700 -11.450800 -11.232000 orl400_005_c -12.502900 -12.835100 -13.148100 orl400_005_d -12.153400 -12.462800 -12.819600 orl400_005_e -12.031500 -12.209600 -12.269300 orl400_005_f -11.716900 -11.647500 -11.316800 orl400_005_g -12.047600 -12.461400 -13.174400 orl400_005_h -13.004400 -13.382900 -13.788600 orl400_005_i -11.760800 -12.086000 -12.374100 orl400_005_j -11.703100 -11.887400 -12.048100 orl400_05_a -8.651410 -8.899220 -9.152470 orl400_05_b -8.403620 -8.788810 -9.288880 orl400_05_c -8.285330 -8.557240 -8.786780 orl400_05_d -8.390980 -8.582550 -8.773230 orl400_05_e -8.001770 -8.109550 -8.163210 orl400_05_f -8.290360 -8.695600 -9.208310 orl400_05_g -8.989910 -9.221480 -9.494270 orl400_05_h -8.578660 -8.929540 -9.293550 orl400_05_i -7.949870 -8.384540 -8.872610 orl400_05_j -8.472860 -8.807480 -9.162090