Lilian

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4 years, 190 days

MaplePrimes Activity


These are replies submitted by Lilian

@Gillee 

Thanks for your answer.
This is interesting... Maybe calling LLSolve function multiple times, adding the previous result as the initialpoint for the next call can be a good way to get better results.

However, I finally managed to get better results by resizing my equations (the D values were really close to 0 so I just added a 1000 factor)

Thanks a lot @phil2 for your detailed answer. However I can't find any attached worksheet, where should I get the attached files ?

Admittedly, this still doesn't quite explain why the new minimum is actually larger.  However, considering that, as you pointed out, the constraints were redundant to begin with, the notion of feasibility tolerance makes those constraints inadvisable anyway.

The problem is that sometimes (depending on the system, which is not always the exact same one as list_1 or list_2) LSSolve comes out with negatives values as D, and I would like to make sure that it never happens, and I guess there is now other way to do that than adding positive constraints. Maybe playing with the feasability tolerance option could lead me to better results?

@phil2 

I am really sorry, I attached the wrong list of equations..

Here is the worksheet :
 

list_1 := [-0.777253031437943e-1+6.57999999999998*D2+(276.680000000000-Phi12_17)*D17, .978053142243381-633.614000000000*D2+(-6.58400000000000-Phi23_17)*D17, -0.178064883733416e-1+253.738100000000*D2+(-5.34190000000000-Phi34_17)*D17, -0.353869747788979e-2+39.4444000000000*D2+(-1.06160000000000-Phi45_17)*D17, -0.884707703096015e-3+9.86159000000000*D2+(-.265410000000000-Phi56_17)*D17, -0.226985309680582e-1+190.480500000000*D2+(-6.80950000000000-Phi67_17)*D17, -0.862540843423853e-3+2.15544000000000*D2+(-.258760000000000-Phi78_17)*D17, -0.141061228211511e-2+2.10972000000000*D2+(-.423180000000000-Phi89_17)*D17, -0.163814759658455e-2+2.45006000000000*D2+(-.491440000000000-Phi910_17)*D17, -0.525504575536290e-2+6.99450000000000*D2+(-1.57650000000000-Phi1011_17)*D17, -0.305389325672901e-1+28.4964000000000*D2+(-9.16160000000000-Phi1112_17)*D17, -0.987175261941468e-1+25.7100000000000*D2+(-29.6150000000000-Phi1213_17)*D17, -0.493604297782517e-2+1.28550000000000*D2+(-1.48080000000000-Phi1314_17)*D17, -0.522437882168112e-1+6.41700000000000*D2+(-15.6730000000000-Phi1415_17)*D17, -.141614566362726+13.9970000000000*D2+(-42.4840000000000-Phi1516_17)*D17, 0.777253031360147e-1-42.4900000000000*D15+(155.450000000000-Phi12_17)*D28, 0.219470855957043e-1-13.9960000000000*D15+(43.8940000000000-Phi23_17)*D28, 0.178065694473007e-1-12.8320000000000*D15+(35.6130000000000-Phi34_17)*D28, 0.353886380190268e-2-2.92230000000000*D15+(7.07770000000000-Phi45_17)*D28, 0.884703450426918e-3-.730700000000000*D15+(1.76940000000000-Phi56_17)*D28, 0.226985885266366e-1-20.8670000000000*D15+(45.3970000000000-Phi67_17)*D28, 0.862553364039491e-3-.965300000000000*D15+(1.72510000000000-Phi78_17)*D28, 0.141060550149453e-2-1.62670000000000*D15+(2.82120000000000-Phi89_17)*D28, 0.163815638896446e-2-1.88900000000000*D15+(3.27630000000000-Phi910_17)*D28, 0.525502049507568e-2-6.09000000000000*D15+(10.5100000000000-Phi1011_17)*D28, 0.305386191034954e-1-35.8000000000000*D15+(61.0770000000000-Phi1112_17)*D28, 0.987153849993141e-1-117.980000000000*D15+(197.430000000000-Phi1213_17)*D28, 0.493586925035572e-2-5.89830000000000*D15+(9.87170000000000-Phi1314_17)*D28, 0.522452037612234e-1-62.6800000000000*D15+(104.490000000000-Phi1415_17)*D28, -.858384447685986+609.990000000000*D15+(283.230000000000-Phi1516_17)*D28, 0.133722502645145e-2-5.34000000000003*D3+(264.760000000000-Phi12_19)*D19, 0.492898645263975e-1-253.740000000000*D3+(373.290000000000-Phi23_19)*D19, -.792605146598487+1386.78000000000*D3+(1127.70000000000-Phi34_19)*D19, .132715839620078-165.954000000000*D3+(-206.460000000000-Phi45_19)*D19, 0.331294375945810e-1-41.4870000000000*D3+(-51.6140000000000-Phi56_19)*D19, .512857041219517-749.640000000000*D3+(-946.930000000000-Phi67_19)*D19, 0.345803892354315e-2-6.58880000000000*D3+(-9.00300000000000-Phi78_19)*D19, 0.253797811562394e-2-5.18510000000000*D3+(-7.71800000000000-Phi89_19)*D19, 0.294701900455624e-2-6.02140000000000*D3+(-8.96290000000000-Phi910_19)*D19, 0.754969755588153e-2-15.8980000000000*D3+(-24.4690000000000-Phi1011_19)*D19, 0.181312716670633e-1-44.7810000000000*D3+(-82.4390000000000-Phi1112_19)*D19, 0.133647518064223e-1-35.1810000000000*D3+(-90.5060000000000-Phi1213_19)*D19, 0.667987641718040e-3-1.75900000000000*D3+(-4.52530000000000-Phi1314_19)*D19, 0.217080361770671e-2-6.75400000000000*D3+(-28.8440000000000-Phi1415_19)*D19, 0.365299883394169e-2-12.8320000000000*D3+(-69.3130000000000-Phi1516_19)*D19, -0.130020251659236e-2+6.81000000000000*D6+(263.430000000000-Phi12_19)*D20, -0.493576878414119e-1+190.470000000000*D6+(323.980000000000-Phi23_19)*D20, -.207482316974689+749.650000000000*D6+(920.260000000000-Phi34_19)*D20, -.132570648903326+410.334000000000*D6+(461.-Phi45_19)*D20, -0.329843798422150e-1+102.583000000000*D6+(115.250000000000-Phi56_19)*D20, .487420161727992-1880.19000000000*D6+(-1459.80000000000-Phi67_19)*D20, -0.345553822678983e-2+26.0430000000000*D6+(-12.4610000000000-Phi78_19)*D20, -0.254139584204717e-2+18.7200000000000*D6+(-10.2570000000000-Phi89_19)*D20, -0.295045955688278e-2+21.7400000000000*D6+(-11.9110000000000-Phi910_19)*D20, -0.755117615405593e-2+55.1470000000000*D6+(-32.0200000000000-Phi1011_19)*D20, -0.181178219908242e-1+124.980000000000*D6+(-100.570000000000-Phi1112_19)*D20, -0.133520796896221e-1+89.6200000000000*D6+(-103.870000000000-Phi1213_19)*D20, -0.668104062372097e-3+4.48110000000000*D6+(-5.19340000000000-Phi1314_19)*D20, -0.217033804692734e-2+13.3910000000000*D6+(-31.0150000000000-Phi1415_19)*D20, -0.365556938318863e-2+20.8670000000000*D6+(-72.9670000000000-Phi1516_19)*D20, 0.135489886901528e-2-.259999999999991*D7+(256.360000000000-Phi12_21)*D22, 0.680675384195741e-2-2.16000000000000*D7+(131.350000000000-Phi23_21)*D22, 0.167104193845212e-1-6.59000000000000*D7+(164.020000000000-Phi34_21)*D22, 0.655190381659506e-2-2.76600000000000*D7+(47.9000000000000-Phi45_21)*D22, 0.163878244157080e-2-.692000000000000*D7+(11.9750000000000-Phi56_21)*D22, 0.603897781618217e-1-26.0400000000000*D7+(394.350000000000-Phi67_21)*D22, -.981708865268294+89.7700000000000*D7+(51.2660000000000-Phi78_21)*D22, .286945758784479-5.67000000000000*D7+(-34.6470000000000-Phi89_21)*D22, .333288992029305-6.58400000000000*D7+(-40.2350000000000-Phi910_21)*D22, .115166403866294-14.3630000000000*D7+(-101.530000000000-Phi1011_21)*D22, 0.796486977999666e-1-12.5100000000000*D7+(-238.060000000000-Phi1112_21)*D22, 0.513893785319347e-1-8.19999999999999*D7+(-201.690000000000-Phi1213_21)*D22, 0.257108190144080e-2-.409500000000000*D7+(-10.0840000000000-Phi1314_21)*D22, 0.486795807939043e-2-.850999999999999*D7+(-45.2570000000000-Phi1415_21)*D22, 0.524862014258993e-2-.965000000000003*D7+(-94.7990000000000-Phi1516_21)*D22, -0.136101769174909e-2+1.57999999999998*D10+(255.450000000000-Phi12_21)*D23, -0.680508845874531e-2+6.99000000000001*D10+(126.790000000000-Phi23_21)*D23, -0.167210744986313e-1+15.9000000000000*D10+(152.820000000000-Phi34_21)*D23, -0.654955044315159e-2+6.04100000000000*D10+(43.5110000000000-Phi45_21)*D23, -0.163599881722489e-2+1.51050000000000*D10+(10.8780000000000-Phi56_21)*D23, -0.603847441196420e-1+55.1500000000000*D10+(353.890000000000-Phi67_21)*D23, -0.182876336377057e-1+14.3600000000000*D10+(39.0120000000000-Phi78_21)*D23, -.286946970814718+35.7040000000000*D10+(83.0820000000000-Phi89_21)*D23, -.333290206967530+41.4630000000000*D10+(96.4820000000000-Phi910_21)*D23, .884841237755273-359.510000000000*D10+(-178.690000000000-Phi1011_21)*D23, -0.796889746454705e-1+94.6100000000000*D10+(-291.440000000000-Phi1112_21)*D23, -0.513575859600819e-1+60.8700000000000*D10+(-236.110000000000-Phi1213_21)*D23, -0.256926809156710e-2+3.04300000000000*D10+(-11.8060000000000-Phi1314_21)*D23, -0.486633264478440e-2+5.69300000000000*D10+(-48.5180000000000-Phi1415_21)*D23, -0.524686208104891e-2+6.08500000000001*D10+(-98.3150000000000-Phi1516_21)*D23, 0.740538677273994e-2-9.16000000000000*D11+(244.710000000000-Phi12_23)*D25, 0.642783571664902e-2-28.4970000000000*D11+(91.3030000000000-Phi23_23)*D25, 0.879545937424008e-2-44.7820000000000*D11+(92.1380000000000-Phi34_23)*D25, 0.267263958813606e-2-14.5080000000000*D11+(22.9620000000000-Phi45_23)*D25, 0.668159897034014e-3-3.62700000000000*D11+(5.74050000000000-Phi56_23)*D25, 0.224071702943972e-1-124.980000000000*D11+(173.760000000000-Phi67_23)*D25, 0.204975705587393e-2-12.5020000000000*D11+(12.1500000000000-Phi78_23)*D25, 0.398190796934755e-2-24.6980000000000*D11+(22.6800000000000-Phi89_23)*D25, 0.462414151228524e-2-28.6810000000000*D11+(26.3380000000000-Phi910_23)*D25, 0.152190448689061e-1-94.6100000000000*D11+(86.2100000000000-Phi1011_23)*D25, -.905930086863230+912.110000000000*D11+(526.060000000000-Phi1112_23)*D25, .687841196392981-376.270000000000*D11+(-673.250000000000-Phi1213_23)*D25, 0.343937963386998e-1-18.8130000000000*D11+(-33.6620000000000-Phi1314_23)*D25, 0.305873475333330e-1-34.1060000000000*D11+(-88.3170000000000-Phi1415_23)*D25, 0.294965405620479e-1-35.8000000000000*D11+(-140.200000000000-Phi1516_23)*D25, -0.740003311264899e-2+15.6700000000000*D14+(213.610000000000-Phi12_23)*D26, -0.643002877220721e-2+6.41700000000000*D14+(64.3070000000000-Phi23_23)*D26, -0.879503935483085e-2+6.75400000000000*D14+(55.1990000000000-Phi34_23)*D26, -0.267001194740175e-2+1.73800000000000*D14+(11.7380000000000-Phi45_23)*D26, -0.668002989087778e-3+.434300000000000*D14+(2.93440000000000-Phi56_23)*D26, -0.224051002552570e-1+13.3910000000000*D14+(79.6550000000000-Phi67_23)*D26, -0.205000917309872e-2+.851000000000000*D14+(3.54140000000000-Phi78_23)*D26, -0.398201781818492e-2+1.50890000000000*D14+(5.95680000000000-Phi89_23)*D26, -0.462402069093096e-2+1.75230000000000*D14+(6.91760000000000-Phi910_23)*D26, -0.152200681046646e-1+5.69300000000000*D14+(22.2930000000000-Phi1011_23)*D26, -0.941004210676048e-1+34.1030000000000*D14+(130.980000000000-Phi1112_23)*D26, -.687853077910222+122.340000000000*D14+(437.750000000000-Phi1213_23)*D26, -0.344056792915157e-1+6.11800000000000*D14+(21.8880000000000-Phi1314_23)*D26, .969399863074721-383.950000000000*D14+(-216.780000000000-Phi1415_23)*D26, -0.295001320031278e-1+62.6800000000000*D14+(-264.080000000000-Phi1516_23)*D26]:

with(Optimization); rep1 := LSSolve(list_1); rep2 := LSSolve(list_1, {D10 >= 0, D11 >= 0, D14 >= 0, D15 >= 0, D17 >= 0, D19 >= 0, D2 >= 0, D20 >= 0, D22 >= 0, D23 >= 0, D25 >= 0, D26 >= 0, D28 >= 0, D3 >= 0, D6 >= 0, D7 >= 0}); rep1 := LSSolve(list_2); rep2 := LSSolve(list_2, {D18 >= 0, D27 >= 0, D29 >= 0, D36 >= 0})

[0.182130325886275e-7, [D10 = HFloat(0.002000093347416389), D11 = HFloat(6.666205093053039e-4), D14 = HFloat(0.0022221520824599844), D15 = HFloat(0.0012820279138359672), D17 = HFloat(0.004998861403449358), D19 = HFloat(3.029255266744349e-4), D2 = HFloat(0.0010000234934204896), D20 = HFloat(1.4284944659735357e-4), D22 = HFloat(0.01111211271354064), D23 = HFloat(0.0022222805411430922), D25 = HFloat(7.142936214972088e-4), D26 = HFloat(8.333263499191028e-4), D28 = HFloat(2.1739653171991575e-4), D3 = HFloat(4.002175679009348e-4), D6 = HFloat(1.6687886220206148e-4), D7 = HFloat(0.009999698285428371), Phi1011_17 = HFloat(-1.228502431180965), Phi1011_19 = HFloat(-20.533519373654585), Phi1011_21 = HFloat(-104.09096431277415), Phi1011_23 = HFloat(19.214449939212358), Phi1112_17 = HFloat(-9.57006175328916), Phi1112_19 = HFloat(-81.68486302365807), Phi1112_21 = HFloat(-242.1498491748034), Phi1112_23 = HFloat(109.00135135008516), Phi1213_17 = HFloat(-44.219748932875795), Phi1213_19 = HFloat(-92.82671959308529), Phi1213_21 = HFloat(-204.44416589041828), Phi1213_23 = HFloat(-61.44476127504735), Phi12_17 = HFloat(262.4476511854361), Phi12_19 = HFloat(262.14919240665415), Phi12_21 = HFloat(256.2484052767522), Phi12_23 = HFloat(246.52117286304335), Phi1314_17 = HFloat(-2.2110615918866032), Phi1314_19 = HFloat(-4.64255435896982), Phi1314_21 = HFloat(-10.221215875683743), Phi1314_23 = HFloat(-3.077984004772912), Phi1415_17 = HFloat(-24.84038315298048), Phi1415_19 = HFloat(-30.594450771890468), Phi1415_21 = HFloat(-45.58470252594737), Phi1415_23 = HFloat(-77.32976800445691), Phi1516_17 = HFloat(-68.01327120138), Phi1516_19 = HFloat(-74.2023324472602), Phi1516_21 = HFloat(-95.1952296374022), Phi1516_23 = HFloat(-132.32846708126223), Phi23_17 = HFloat(62.31653108816923), Phi23_19 = HFloat(200.80422545113467), Phi23_21 = HFloat(130.01879159887292), Phi23_23 = HFloat(73.70432624302144), Phi34_17 = HFloat(41.85634777007731), Phi34_19 = HFloat(343.4099879320013), Phi34_21 = HFloat(159.59399606138695), Phi34_23 = HFloat(62.656475770029026), Phi45_17 = HFloat(6.121364130365998), Phi45_19 = HFloat(12.383917194570708), Phi45_21 = HFloat(46.000528179934825), Phi45_23 = HFloat(13.166579651635805), Phi56_17 = HFloat(1.530420688109261), Phi56_19 = HFloat(3.166146874145713), Phi56_21 = HFloat(11.499811489254649), Phi56_23 = HFloat(3.2909339469103527), Phi67_17 = HFloat(26.75542459204723), Phi67_19 = HFloat(-244.28897794294045), Phi67_21 = HFloat(376.3514935402879), Phi67_23 = HFloat(88.48304651883907), Phi78_17 = HFloat(-1.1056208585550253e-4), Phi78_19 = HFloat(-6.280613803912376), Phi78_21 = HFloat(43.70358459671294), Phi78_23 = HFloat(3.3512347369068123), Phi89_17 = HFloat(-0.28331633046782223), Phi89_19 = HFloat(-6.188115079131574), Phi89_21 = HFloat(-13.925822440131276), Phi89_23 = HFloat(5.203255725370639), Phi910_17 = HFloat(-0.32900739184223554), Phi910_19 = HFloat(-7.185809707858909), Phi910_21 = HFloat(-16.1669897157201), Phi910_23 = HFloat(6.042912241714565)]]

 

Warning, limiting number of major iterations has been reached

 

[0.667302976414868160e-1, [D10 = HFloat(0.002401994423790786), D11 = HFloat(6.665775721335379e-4), D14 = HFloat(0.0022221878679006186), D15 = HFloat(0.0012819244175765116), D17 = HFloat(0.002786788890567199), D19 = HFloat(2.0047331771968024e-4), D2 = HFloat(0.0010993853815580601), D20 = HFloat(8.407217626499022e-5), D22 = HFloat(6.857704827265397e-4), D23 = HFloat(-1.38753085778e-312), D25 = HFloat(7.143977336270289e-4), D26 = HFloat(8.332012323392386e-4), D28 = HFloat(2.0431973185161233e-4), D3 = HFloat(4.1999401587211187e-4), D6 = HFloat(1.9199690986289393e-4), D7 = HFloat(0.010388450531904679), Phi1011_17 = HFloat(-0.7097073355930499), Phi1011_19 = HFloat(-15.78639758968181), Phi1011_21 = HFloat(-151.17184370855747), Phi1011_23 = HFloat(19.221140903034335), Phi1112_17 = HFloat(-8.9060467628395), Phi1112_19 = HFloat(-75.86275393829612), Phi1112_21 = HFloat(-311.4239309672987), Phi1112_23 = HFloat(109.00288065092703), Phi1213_17 = HFloat(-54.92123651946663), Phi1213_19 = HFloat(-89.97905650929866), Phi1213_21 = HFloat(-250.9716717560008), Phi1213_23 = HFloat(-61.51600033356302), Phi12_17 = HFloat(251.48087251588103), Phi12_19 = HFloat(255.97757300650363), Phi12_21 = HFloat(254.39710089135374), Phi12_23 = HFloat(246.52467236615772), Phi1314_17 = HFloat(-2.746143863288059), Phi1314_19 = HFloat(-4.484018225386535), Phi1314_21 = HFloat(-12.538157234477064), Phi1314_23 = HFloat(-3.0815449128056702), Phi1415_17 = HFloat(-31.89475142521548), Phi1415_19 = HFloat(-30.80904005123437), Phi1415_21 = HFloat(-51.04991967695345), Phi1415_23 = HFloat(-77.32689692295996), Phi1516_17 = HFloat(-87.79477904885191), Phi1516_19 = HFloat(-75.54030052465637), Phi1516_21 = HFloat(-101.76377136447809), Phi1516_23 = HFloat(-132.31452439322106), Phi23_17 = HFloat(94.00935908490689), Phi23_19 = HFloat(86.44297570258689), Phi23_21 = HFloat(108.55476500416788), Phi23_23 = HFloat(73.70722794312684), Phi34_17 = HFloat(87.69389243714414), Phi34_19 = HFloat(82.39223477535546), Phi34_21 = HFloat(88.55820786368487), Phi34_23 = HFloat(62.66040780511909), Phi45_17 = HFloat(13.191019806012159), Phi45_19 = HFloat(69.3008595136826), Phi45_21 = HFloat(15.553098356671507), Phi45_23 = HFloat(13.167768155968398), Phi56_17 = HFloat(3.2979207216953395), Phi56_19 = HFloat(17.40033492720939), Phi56_21 = HFloat(3.881876329175012), Phi56_23 = HFloat(3.2912311513338337), Phi67_17 = HFloat(60.00457070362334), Phi67_19 = HFloat(54.30708686261723), Phi67_21 = HFloat(87.94212888028821), Phi67_23 = HFloat(88.49299201250949), Phi78_17 = HFloat(0.2799521863118858), Phi78_19 = HFloat(-3.50632712699654), Phi78_21 = HFloat(-20.387216720331548), Phi78_23 = HFloat(3.3521374864201916), Phi89_17 = HFloat(-0.09912991698285016), Phi89_19 = HFloat(-4.446366838430626), Phi89_21 = HFloat(297.88881192632755), Phi89_23 = HFloat(5.205006716614384), Phi910_17 = HFloat(-0.11510170055567215), Phi910_19 = HFloat(-5.166037617767921), Phi910_21 = HFloat(346.0333512916284), Phi910_23 = HFloat(6.0449456431082575)]]

 

Warning, limiting number of iterations reached

 

[0.173158517170151e-3, [D18 = HFloat(4.940399971912688e-4), D27 = HFloat(3.123022055695685e-4), D29 = HFloat(0.012053079546584859), D36 = HFloat(-0.02877258006663398), Phi1011_18 = HFloat(-10.047440876654184), Phi1011_24 = HFloat(-4.89440481171543), Phi1112_18 = HFloat(-58.20988683846057), Phi1112_24 = HFloat(-29.338754572925264), Phi1213_18 = HFloat(-83.08949138713488), Phi1213_24 = HFloat(-56.12110719411204), Phi12_18 = HFloat(260.26860758672166), Phi12_24 = HFloat(263.20617377185454), Phi1314_18 = HFloat(-3.4457440384526827), Phi1314_24 = HFloat(-2.5087129560312764), Phi1415_18 = HFloat(-32.549935720740386), Phi1415_24 = HFloat(-25.48888809044497), Phi1516_18 = HFloat(-72.10104065466892), Phi1516_24 = HFloat(-62.675427552811946), Phi23_18 = HFloat(89.12923249096826), Phi23_24 = HFloat(61.483196901345444), Phi34_18 = HFloat(125.54530604503496), Phi34_24 = HFloat(68.67880838477211), Phi45_18 = HFloat(13.68255794893495), Phi45_24 = HFloat(8.04368413990329), Phi56_18 = HFloat(2.919597731660753), Phi56_24 = HFloat(1.8129257306833229), Phi67_18 = HFloat(24.210838638941365), Phi67_24 = HFloat(20.01451125467167), Phi78_18 = HFloat(-1.4701283478035998), Phi78_24 = HFloat(-0.6483549804256254), Phi89_18 = HFloat(-2.559740721298145), Phi89_24 = HFloat(-1.2378238951622822), Phi910_18 = HFloat(-2.938954535723053), Phi910_24 = HFloat(-1.4230779501001942)]]

 

Error, (in Optimization:-LSSolve) no improved point could be found

 

``

Download worksheet_help(1).mw

 

I don't understand, why when adding constraints for List_1, i get a worse result.
List_2 should be resolvable as well, but the result I get without any constraint is not correct (D36 is negative), and when I add positive constraints, LSSolve returns an error....

I am using Maple 2016.0

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