如何避免在Julia中使用NLsolve解决问题的过程中使用幂函数的负基？

我是个初学者。我想用nlsolve解以下非线性方程

#Variables 
D= 200 #number of dimension
w= [0.17935458155165915; 0.02074763117110885; 0.429373018098153; 0.05169130596707894; 0.1268251892348001; 0.28504924497346273; 0.2653879531047568; 0.28907305874421907; 0.3211732529510658; 0.19640464810886332; 0.23743064655310908; 0.31271077337877673; 0.48784812550619117; 0.46951525260820676; 0.414672793999191; 0.2568327281950456; 0.04655836280984356; 0.3553694395191944; 0.0961544234898889; 0.36088980496765105; 0.37309711801193857; 0.47543051066838987; 0.27729500688542985; 0.3655300449541484; 0.16055046782127508; 0.4715786828535815; 0.2921904371516787; 0.0867716272042234; 0.02458893193755404; 0.40826853858704576; 0.13564939368933704; 0.08565749854632393; 0.06533558241443299; 0.06402050462910032; 0.3671937923414826; 0.1720370049889512; 0.5002983463084618; 0.4554957808473552; 0.46517364874849754; 0.1212216024211966; 0.04284454643266707; 0.37915786950647656; 0.17464050734498965; 0.21533246021336955; 0.05582083301947215; 0.01890049888476679; 0.06796265527558022; 0.13497310074129715; 0.20160681047548307; 0.30315821352156913; 0.3251250459650451; 0.07933939439789317; 0.05474492295189952; 0.04305583367874512; 0.4361224247290211; 0.16432217073350208; 0.31303482284024337; 0.4451670195690176; 0.19978224229965896; 0.005269209445990741; 0.5169890042928693; 0.49791983700852965; 0.017989427943135895; 0.20315428046276351; 0.06689193239618459; 0.3680050603415692; 0.04551910758173742; 0.01662604468426492; 0.06004114983952084; 0.4478453864302301; 0.39411123774712575; 0.3094838485413219; 0.33815112721353957; 0.4240423855967578; 0.12932548776099762; 0.29086619751681675; 0.4030396981865735; 0.5054293368932627; 0.47285161364574857; 0.3098801558764114; 0.16515650220976294; 0.503913510788379; 0.4088656755934767; 0.22986629914797763; 0.18001932518476532; 0.33046480913959986; 0.23212104534106723; 0.2803414905211751; 0.5049525882832877; 0.08521812980417476; 0.4069606921394297; 0.2181371065953835; 0.053727840369329705; 0.17617975359933452; 0.4694543012021901; 0.34756349021452404; 0.48518448761421923; 0.02368032680125083; 0.490453983772221; 0.29518522250300117; 0.029269655059924668; 0.10399922894246545; 0.36353617514053105; 0.03387829393121781; 0.025490776554460855; 0.4310812832361403; 0.028795585312659543; 0.4933248156252178; 0.3656192375750969; 0.4589261148594532; 0.3288070975147629; 0.040785776187926344; 0.5022914836438017; 0.5160150437151949; 0.5242657868366228; 0.34618308317731006; 0.1319908503735835; 0.47195419822851153; 0.05207014105918679; 0.19467771783330873; 0.49166830880087564; 0.13531702218739206; 0.1823017910366312; 0.030660444370685203; 0.3962884724121194; 0.25086570699970984; 0.3959784732876863; 0.1641317515418158; 0.07964603629529568; 0.26417075311032945; 0.393654266782284; 0.20930682065612094; 0.05653175390672894; 0.37420934462301003; 0.23460192018381498; 0.46636742061631675; 0.14086364242937774; 0.08161750625372813; 0.4862927691208331; 0.05356082693328593; 0.5055848873287434; 0.028812527866598325; 0.18581121132195139; 0.43018487478885936; 0.4473538614535335; 0.4583871013830452; 0.0412195586331303; 0.03141717976980104; 0.4676441420752301; 0.034581891245706556; 0.36771481416639373; 0.4515357316321425; 0.13797591008597196; 0.026251893538842566; 0.03795891476862359; 0.029165568365405; 0.105839838518907; 0.5078856492325493; 0.2576434906126355; 0.31916462500676; 0.05572200820553658; 0.5307195502657114; 0.35363316006975987; 0.3449622649355296; 0.04727417005006297; 0.20715891655792446; 0.3304136066693219; 0.34214236013075755; 0.13725527724782474; 0.4194480554053426; 0.43190606219458283; 0.4925351054148299; 0.0368272519895124; 0.037005236939482836; 0.05482024474064293; 0.4658322939791588; 0.04183361864909097; 0.2819231154532247; 0.3071668925286857; 0.203845596772382; 0.039560321686506805; 0.08843817736989967; 0.44467968454990625; 0.16610048417579049; 0.4144496080954068; 0.39129200825792365; 0.3821227311795474; 0.40997465387715437; 0.15714005965819433; 0.30726849530055533; 0.4465691501738437; 0.10298380183276976; 0.10168582441320018; 0.030435150474560184; 0.13526831068591066; 0.3811373848822741; 0.39583398602024567; 0.3564651897756602; 0.045102997790797995; 0.06510548733856235]
ε = 6.83
B= [1.9113880593260923; 8.883378033508055; 1.5206988306259004e-20; 0.12873546853181547; 0.037433247431133146; 5.02095391224869e-152; 1.4869904879595479e-49; 4.511864438683239e-21; 2.1083439669659596e-12; 1.573705822018202e-20; 1.3453053264248006e-77; 1.5127934067991649; 4.717077633858784e-15; 3.4700877943503913e-16; 1.3322445962118157e-8; 11.06063549629749; 22.527098400242068; 1.2856792580100785e-26; 18.906029147573; 0.000655510993151066; 10.817043057533661; 0.016479254141517467; 27.298101247774202; 9.148687139608766e-23; 28.441081060976; 5.827459408920411e-9; 0.015917609194167417; 5.921299277490823; 15.131095232259607; 4.5221452182504495e-101; 0.3745605564474358; 35.22790120220832; 26.472693215422034; 15.748913895092457; 13.900215150506208; 0.6656796732438512; 1.0610761914228794e-166; 0.02034815783200824; 6.94235044611682e-21; 3.024382319727409; 4.403762322109802; 19.642152609916533; 0.312733600677696; 7.0450348072031685; 2.9943360410894515; 0.020386834152167167; 5.019796883409017; 1.953805941833118e-42; 26.218829427864886; 1.1679909471382518e-12; 4.700747703804262e-158; 0.739539471301838; 0.03947830752271118; 8.191358248239432; 9.382504981038742e-54; 0.16010589376742393; 0.009015716607052703; 3.637358355198932e-20; 27.327796808642322; 0.8004499183860179; 8.461125192766686e-18; 8.95910135749446e-14; 0.46263795683695763; 3.724763235623522e-29; 0.4627651339879373; 2.1317843123017353; 19.72612759625619; 7.121514602205041; 0.7498244950119917; 7.82776792212211e-29; 2.058164763314051e-48; 6.656376841007709e-110; 1.0185480326011094e-8; 1.0966196183164407e-40; 3.81587425576929; 17.022148683535356; 2.8781418780364653e-226; 6.283831883355779e-60; 7.103441240122817e-17; 1.7971618832549945e-128; 18.528854800853065; 4.497936571326762e-42; 5.9611599404636495; 9.131948748136594; 2.138817581505318; 6.963672986053975e-141; 0.005445679519556468; 1.6679405650005341; 2.3337652049764904e-22; 1.419494251779325; 2.261935115923545e-46; 1.2376566162579915e-32; 4.328787591872048; 5.844233889688261e-7; 8.830924221173814e-34; 4.377778889817346e-81; 1.8878051058094012; 0.2998408805976853; 3.9392863709967796; 2.8084798567644255e-7; 0.14707594960663317; 38.59529055572117; 5.209103347927197e-21; 0.0025973623652913317; 1.5593014209459997; 1.3107443853139182e-21; 5.179647971121189; 3.236157265411051e-16; 7.093888840049452e-26; 1.5564589470829775e-71; 0.001741657884835898; 2.627144619341441; 0.04548803609276873; 2.4673234325112487e-29; 1.3507640402698248e-87; 4.38379124625374e-107; 19.316618329311616; 1.2877899257156492e-8; 22.33866240442435; 7.477065799186867; 1.7971426221661947e-49; 3.3345318772733243; 1.603348886130618; 9.19752238851656; 6.356526861225398e-67; 18.93162033259596; 1.2485391021861125e-98; 17.39152256819622; 0.891805611066936; 35.20596843419915; 1.6898318496500515; 5.638826369435781e-41; 1.2229640299979205; 1.6370815943900768e-74; 0.9756549709108758; 1.3904665924398121e-6; 1.8582909404291397; 1.9869657417523816; 9.819641204968615e-5; 11.71516179379171; 2.226782016861399e-7; 2.0750601055907887; 2.1347726595107657e-10; 1.683191425244726e-46; 2.3584667613037514e-16; 18.624750803153773; 17.12056336027302; 0.36126716256726055; 1.2788867483362755e-118; 1.532524744507334; 5.252933249817591e-44; 4.136636658945092e-32; 0.43950895342231955; 6.120212273528275; 0.987566032480816; 10.027807407458246; 0.34575101054546964; 4.261326022977069e-24; 9.140183928737398e-71; 7.162942951718289; 2.582956434666498; 2.9453506559779514e-10; 18.472793617032533; 7.085056386755511e-12; 36.40227058129134; 0.13079840647173033; 5.7395520820424e-69; 7.839955677157711e-62; 3.817437369660718e-33; 3.6404078004251237e-261; 1.252788930584791e-60; 1.8439518176020697e-42; 3.7077748286865955; 10.923507699176934; 4.398723765471304; 37.00277456879605; 7.163775800693194; 3.042070021429068e-36; 1.133732867786907e-27; 8.471981021660175; 17.313578618750533; 29.52963937643628; 1.6883607661890261e-18; 16.675675294485313; 8.083285501565638e-116; 1.7856881885430648e-71; 7.554472386121312e-6; 2.959280305979924e-54; 0.47485862974337695; 43.64815259851988; 0.00020435835048960367; 4.178015918890087; 0.7154468290561525; 19.95948484510194; 5.121764686065876; 1.4777202796969108e-44; 4.6531581853388824e-32; 4.262223219325753e-77; 10.910140454174218; 2.3511019348088893]
C= [0.02236367582581154; 9.58383778144876e-9; 10.622999409755542; 6.16241579726002e-6; 0.0018032815929029718; 0.5820246596178108; 0.46011206498448826; 0.7889991211217988; 1.4684689617091775; 0.05302456476377496; 0.10653991490875167; 0.8187437238615558; 21.42099755745115; 14.532608506948357; 7.130677101093516; 0.2695827025367284; 2.840960239678163e-6; 2.6149971669855403; 0.0002862249023265326; 2.206551045659344; 3.201701648734815; 15.84638486786215; 0.42036030490492404; 1.6441067874030098; 0.007690277824884048; 13.4229674661184; 0.776815090305774; 0.00017622198806910893; 4.047911673106026e-8; 8.52074610887776; 0.0015589533591112501; 0.00019850233659576524; 3.451312792433583e-5; 2.2765682832796673e-5; 3.4658361107945646; 0.02240030876897966; 21.24634498913638; 14.886659535117845; 20.331597580089422; 0.0015512506515751182; 1.1473872576179618e-6; 4.463818741209099; 0.024558108769859248; 0.08003730285262999; 1.0245101733923846e-5; 4.810690364785042e-9; 3.8449023058738855e-5; 0.004656842074317859; 0.05215675661535674; 0.8754064652759576; 1.3659241825975006; 0.00010536064903923549; 6.815257400995486e-6; 1.6332498205461194e-6; 14.838232003036559; 0.014148116381231153; 1.0747805759685072; 13.735602775324027; 0.05821913419275878; 7.072971977150658e-13; 36.085053287224845; 24.234945337082472; 3.775435520586117e-9; 0.06754539214330033; 3.5509190137439215e-5; 3.5579316268225694; 2.9411447208169765e-6; 2.5133421674066183e-9; 1.5062541187856675e-5; 14.694661779281075; 6.897268288709871; 0.7043989278476316; 1.9167230320590787; 10.073132706193185; 0.0028524971206745826; 0.6830477988007796; 6.521786417021922; 21.39217680761771; 17.141148981019942; 0.8465190498941498; 0.017625871401570122; 37.530744437384; 6.981342810181801; 0.12553899875906288; 0.02373963846881343; 1.344559849850729; 0.1690456323666673; 0.5512783866374767; 35.36197200806055; 0.0001408808253739378; 7.3508161565003585; 0.10860528902466145; 7.2717212309772544e-6; 0.016522549776560022; 16.473016905351493; 2.6127833707757824; 28.271280477163984; 3.3312692063423355e-8; 19.994267776549698; 0.6657430297670275; 1.0123785359436453e-7; 0.0006714142571638888; 2.4800026677881197; 3.382125591220219e-7; 4.7115287960519034e-8; 9.525619254857425; 8.271785513563928e-8; 21.490119694933856; 2.5062610399242327; 14.608813232400994; 1.8841651678257887; 8.421086239731675e-7; 28.750558264884454; 15.462293619736093; 29.46282215646338; 2.7066671596653933; 0.002592176417467211; 16.927305215283532; 5.655929890117654e-6; 0.04185013906013212; 23.089441205413877; 0.004178233766777603; 0.0278435050258412; 1.7453606686033147e-7; 4.569441678495397; 0.2937225655189823; 6.0288522810291365; 0.009970572371840814; 0.00010933874610531001; 0.48682413706500893; 6.207955072097215; 0.08854058360680914; 8.12806476837625e-6; 2.2342992920598417; 0.0711867387607783; 20.429841948532424; 0.0029902989914194706; 5.159006124218317e-5; 24.856022732116386; 5.7161295515373945e-6; 21.593135919447022; 1.034593572589091e-7; 0.03432570558664665; 11.8662784181379; 14.064150052406164; 16.58378730247712; 1.4641109475465026e-6; 1.513379889790401e-7; 13.486193224640694; 2.3415045686879677e-7; 1.7274421009808538; 17.664229193215167; 0.00401027321008269; 5.362881287338797e-8; 5.149019194174631e-7; 1.0329083624982976e-7; 0.0006822794649301988; 20.346835250844983; 0.2636146568801335; 1.1869695390218922; 9.279107770625925e-6; 19.249201278261733; 2.8466949459082866; 2.334280646591445; 2.5958954067544824e-6; 0.02604700360517058; 1.6444095893601727; 1.8524998416755938; 0.004535053868363867; 8.402808209415497; 10.821421853057345; 10.71048783445611; 5.708352034806126e-7; 4.4951717518111495e-7; 3.980711719757998e-6; 19.796380459889406; 1.2375725596404167e-6; 0.4824144273681875; 0.5732515483334024; 0.0646340619070183; 9.772350730146414e-7; 0.0002754947154589728; 12.308915197976354; 0.01706939966443881; 8.629220990605731; 5.029702735627101; 4.556678536635026; 6.743800116781311; 0.004807381626578681; 1.0724061894701296; 13.221076988100998; 0.0005047754753299702; 0.0004606181382141919; 1.1269545306708471e-7; 0.004833714336739734; 4.087813188584282; 3.054096162953476; 3.4826092556609756; 2.5451852316521397e-6; 2.664488740692585e-5]

#Function
function eq!(F,w)
    numer = w.^ε 
    denomi = sum(numer,dims=2)
    prob = numer./denomi
    F[1:D]=(B'*prob)'-C
end

result=nlsolve(eq!,ones(S))

然后，我得到了以下错误

DomainError with -0.26327276428720575:
Exponentiation yielding a complex result requires a complex argument.
Replace x^y with (x+0im)^y, Complex(x)^y, or similar.

我假设发生错误是因为

w

的某些组件在问题解决过程中变为负值。 因此，我修改了上述方程如下，并使

w

的分量在问题解决过程中取正值

function eq_new!(F,w)
    if sum(w.<=0)==0
        numer = w.^ε 
        denomi = sum(numer,dims=2)
        prob = numer./denomi
        F[1:D]=(B'*prob)'-C
    else
        F[1:D].= sum(abs.(w[w.<=0]))+100
    end
end

result=nlsolve(eq_new!,ones(S))

功能均衡新！（F，w）
如果是sum（w），由于您当前的规范不起作用，您能否通过一个完全可复制的示例。典型的技巧是用
（w.^2）替换
w.^ε
.^ε
，但我无法在没有工作代码的情况下进行测试。当然，获得的解决方案也应该进行转换。当我遇到上述问题时，我指定了变量。
S
仍然没有指定，但我猜它是
200
。但即使您设置了它，那么
（B'*prob）“-C
将不起作用，因为您尝试操作的矩阵的大小不匹配。如果是
（B'*prob）”。-C
？但很明显，由于
C
不是常数，而
B'*prob
是常数，解算器将不会收敛。
Results of Nonlinear Solver Algorithm
 * Algorithm: Trust-region with dogleg and autoscaling
 * Starting Point: [1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0]
 * Zero: [NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN, NaN]
 * Inf-norm of residuals: 1.203524
 * Iterations: 1000
 * Convergence: false
   * |x - x'| < 0.0e+00: false
   * |f(x)| < 1.0e-08: false
 * Function Calls (f): 1000
 * Jacobian Calls (df/dx): 172