Test.mw
I have this data (see attached worksheet). I then run the below code
and then I get the output (see below). The problem is that I have explicity
stated in constraints 3 (con3) that w[i] should be larger than or
equal to zero. Still I get negative solution ie w[1]=-1.47*10^(-18).
Why is that?
The funny thing is that when I change constraint 3 to w[i]>=0.01 then I get :
Error, (in Optimization:-QPSolve) no feasible solution found
Something is very fishy here!
W := Vector[column]([seq(w[i], i = 1 .. NC)]):
ER := Vector[column]([seq(ExpectedValue(Column(RR, i)), i = 1 .. NC)]):
Q := CovarianceMatrix(RR):
con1 := add(w[i], i = 1 .. NC) = 1:
con2 := seq(w[i] <= 1, i = 1 .. NC):
con3 := seq(w[i] >= 0, i = 1 .. NC):
ob := expand(Transpose(W).Q.W):
QPSolve(ob, {con1, con2, con3}, maximize = true);
[16213.6702099999, [w[1] = -1.47967632624492062*10^(-18), w[2] = 3.87788941241543736*10^(-18), w[3] = 6.57295117942385646*10^(-18), w[4] = -2.58184032753756092*10^(-18), w[5] = -8.86592447176614388*10^(-20), w[6] = -4.71769979859663791*10^(-18), w[7] = -3.07424713538522872*10^(-18), w[8] = -6.61548493042091160*10^(-18), w[9] = -7.51897594232547093*10^(-18), w[10] = 1.05225857918290370*10^(-18), w[11] = 2.24223412781379289*10^(-18), w[12] = 1.47265759276968452*10^(-17), w[13] = 7.56763614831905806*10^(-18), w[14] = 1.13307102280914385*10^(-17), w[15] = 6.34918004374760714*10^(-18), w[16] = 1.72211477160568754*10^(-17), w[17] = -2.59565741933960176*10^(-18), w[18] = 5.81678851669601453*10^(-18), w[19] = -1.13538416715036419*10^(-17), w[20] = -1.08925033052168600*10^(-17), w[21] = -1.44018461317300882*10^(-17), w[22] = -1.17739268182037652*10^(-17), w[23] = -3.91854552534047844*10^(-18), w[24] = 1.46228228597826104*10^(-17), w[25] = 2.52700526772569516*10^(-18), w[26] = 1.04278958854746116*10^(-17), w[27] = 8.41697271882256976*10^(-18), w[28] = 7.21420921661147626*10^(-18), w[29] = 3.82717575035324775*10^(-18), w[30] = 3.51614782196505819*10^(-18), w[31] = -2.00112809441533711*10^(-17), w[32] = 1.57013904020523132*10^(-17), w[33] = 3.71608213775887323*10^(-18), w[34] = 4.73441688173662413*10^(-18), w[35] = 7.96758509613566848*10^(-18), w[36] = -2.20560996310134371*10^(-18), w[37] = 8.84125108990355318*10^(-19), w[38] = 1.12531168917894907*10^(-17), w[39] = -1.89529539062730526*10^(-17), w[40] = 3.62169217602425669*10^(-18), w[41] = -1.38146393109072944*10^(-17), w[42] = 3.43072283751421877*10^(-18), w[43] = 5.94456712162712660*10^(-18), w[44] = 1.22677388778037133*10^(-17), w[45] = -1.62699213801088807*10^(-17), w[46] = -9.23684643658690736*10^(-18), w[47] = 3.56083867342727444*10^(-19), w[48] = -1.51008651007352015*10^(-17), w[49] = 2.14247792763123060*10^(-17), w[50] = 2.36849506007516172*10^(-17), w[51] = 7.33307302158499620*10^(-18), w[52] = -4.24925800761836554*10^(-18), w[53] = 6.78213714154721886*10^(-21), w[54] = 2.09156650738168646*10^(-18), w[55] = 1.00872493377525859*10^(-17), w[56] = -1.73963314426017869*10^(-17), w[57] = 5.21319417194942819*10^(-18), w[58] = -1.94159681852454693*10^(-17), w[59] = -8.07966980596961266*10^(-18), w[60] = 1.30908058714328347*10^(-17), w[61] = .99999999999999778, w[62] = -1.06392749991918552*10^(-18), w[63] = 6.55471754833086164*10^(-19), w[64] = -2.90678045784685247*10^(-19), w[65] = 5.85438614164964460*10^(-19), w[66] = 5.80981405681672427*10^(-19), w[67] = -2.00113246956034868*10^(-18), w[68] = 1.53258453231580071*10^(-19), w[69] = 8.67425418163182558*10^(-19), w[70] = -1.02089599282402444*10^(-18), w[71] = -1.03391660367419941*10^(-18), w[72] = -5.83005045331272312*10^(-19), w[73] = -2.89903143422829272*10^(-19), w[74] = 9.53463140177573717*10^(-19), w[75] = -8.82844733457391671*10^(-19), w[76] = -1.55293270314862894*10^(-18), w[77] = -4.24307646237879365*10^(-19), w[78] = -1.52903135037975130*10^(-18), w[79] = 5.90531660546034087*10^(-19), w[80] = -2.21088000284298543*10^(-18), w[81] = -3.59963684152462894*10^(-18), w[82] = -7.35327194285165948*10^(-19), w[83] = -1.42117693001421440*10^(-18), w[84] = -1.34127907023785791*10^(-18), w[85] = -2.22716851109875597*10^(-19), w[86] = 9.17287650545937492*10^(-19), w[87] = -8.32363082623944463*10^(-19), w[88] = 3.60290006479633941*10^(-19), w[89] = -1.09321506050773616*10^(-18), w[90] = -1.02054515072698724*10^(-18), w[91] = -8.59051020972028518*10^(-19), w[92] = -2.13829101605680476*10^(-18), w[93] = -2.10672686340569788*10^(-18), w[94] = -8.74272499173326526*10^(-19), w[95] = 2.26752057687433314*10^(-19), w[96] = 6.77857647871542212*10^(-19), w[97] = 7.18150888657915226*10^(-19), w[98] = 4.09403992256638840*10^(-19), w[99] = -6.14296573255321898*10^(-19), w[100] = -7.35196389306330502*10^(-19), w[101] = 5.68605300914949764*10^(-19), w[102] = 1.59471728218462604*10^(-18), w[103] = 9.91930939888049816*10^(-19), w[104] = -1.05995198187800464*10^(-18), w[105] = -8.28507236698528426*10^(-19), w[106] = 1.17676249343224878*10^(-18), w[107] = -9.49658190705781592*10^(-19), w[108] = -3.23176909456676535*10^(-19), w[109] = -4.94953516030979056*10^(-20), w[110] = 3.85179028670098356*10^(-19), w[111] = 1.45020453842171106*10^(-19), w[112] = 1.99622252373006002*10^(-18), w[113] = -9.62873754744852772*10^(-20), w[114] = 1.53853382978556185*10^(-19), w[115] = -3.13572848582978415*10^(-19), w[116] = -2.19480242527191480*10^(-18), w[117] = -9.36946276525878722*10^(-19), w[118] = 1.95978244247739084*10^(-18), w[119] = -7.83203044883773357*10^(-19), w[120] = -1.28297809114790022*10^(-18), w[121] = 4.45097940460687992*10^(-19), w[122] = 1.19286693221159386*10^(-18), w[123] = 8.12655579543047642*10^(-19), w[124] = 1.73403261673576513*10^(-19), w[125] = 1.97431962450293156*10^(-18), w[126] = 3.64438912528778839*10^(-18), w[127] = 1.24504757294417278*10^(-18), w[128] = -3.27019791834778176*10^(-19), w[129] = 3.17579031658664452*10^(-18), w[130] = 7.35446627924209266*10^(-19), w[131] = 1.48993153121517604*10^(-18), w[132] = -5.88017766095470010*10^(-19), w[133] = 4.74261054365446508*10^(-19), w[134] = 1.78212736808599958*10^(-18), w[135] = -1.12640091501356329*10^(-19), w[136] = -3.58969354390751992*10^(-18), w[137] = -3.63242601065765147*10^(-19), w[138] = 2.31485275490262017*10^(-18), w[139] = -2.51508981536297755*10^(-18), w[140] = 2.36888557632397038*10^(-18), w[141] = 3.65563654712503046*10^(-20), w[142] = 4.77330264938068414*10^(-18), w[143] = 9.28028999047804530*10^(-19), w[144] = -2.76621649438547240*10^(-18), w[145] = -3.71083392212544707*10^(-18), w[146] = 4.17746433452868204*10^(-19), w[147] = -7.54299200196668715*10^(-19), w[148] = 2.50806415509201265*10^(-18), w[149] = -2.96283640105695076*10^(-19), w[150] = 2.34273645039419197*10^(-18), w[151] = -1.33379326125751698*10^(-18), w[152] = -8.65743864412886438*10^(-19), w[153] = -4.16401020806475244*10^(-18), w[154] = 1.75542834447633588*10^(-18), w[155] = -6.59335975079705142*10^(-18), w[156] = 6.08267981542479342*10^(-19), w[157] = -8.25379662177465924*10^(-18), w[158] = 3.09038284197180890*10^(-18), w[159] = -3.51254732441152667*10^(-18), w[160] = -7.07148957880189754*10^(-18), w[161] = -2.87439216530691968*10^(-18), w[162] = 5.80269547101820929*10^(-19), w[163] = -2.91174642648856376*10^(-18), w[164] = 6.74017137609935054*10^(-18), w[165] = -4.66917008489845456*10^(-19), w[166] = -3.98574535208814774*10^(-18), w[167] = 3.36370819067856538*10^(-18), w[168] = -7.20962700663878188*10^(-20), w[169] = -1.95752922775481712*10^(-18), w[170] = 7.88391749654099594*10^(-18), w[171] = 3.57514376387569680*10^(-18), w[172] = 1.68414254157182360*10^(-18), w[173] = -1.79172390814236464*10^(-18), w[174] = 1.58030262895067362*10^(-18), w[175] = -1.01595772436306063*10^(-18), w[176] = -4.45976648314478512*10^(-18), w[177] = -5.53507953314467571*10^(-18), w[178] = 1.16833721717816656*10^(-17), w[179] = -5.20417042793042128*10^(-18), w[180] = 1.22788379582278765*10^(-18), w[181] = -4.52695057709504747*10^(-18), w[182] = 3.89242172406122650*10^(-18), w[183] = -9.82372024103869660*10^(-18), w[184] = -9.06135905396116756*10^(-18), w[185] = 2.28580934528185894*10^(-17), w[186] = 1.93548126570747161*10^(-17), w[187] = 2.64787588989357334*10^(-18), w[188] = 2.02226929975021874*10^(-17), w[189] = 2.42861286636752994*10^(-17), w[190] = 1.17930340516376184*10^(-17), w[191] = 7.40510980537873220*10^(-18), w[192] = -5.00403606684803908*10^(-18), w[193] = 3.25505821650542882*10^(-17), w[194] = 2.53435504813379500*10^(-17), w[195] = 1.70602185556850802*10^(-17), w[196] = -2.56132198896801920*10^(-17), w[197] = -1.18102821194074246*10^(-17), w[198] = 1.44424115021307317*10^(-16), w[199] = 0.]];
