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1、第四章，最优化与存储模型实验4.2，基本实验1.非线性最小二乘问题解：由题可以得出：（1）最小二乘法，分别用x、y代替ξ、η平方和的形式时的lingo程序：sets:quantity/1..15/:x,y;endsetsmin=@sum(quantity:(b*2.71828^(c*x)+a-y)^2);@free(a);@free(b);@free(c);data:x=257101419263134384552536065;y=54504537352520161813811846;enddata运行
2、程序后可以得出：Localoptimalsolutionfound.Objectivevalue:44.78049Infeasibilities:0.000000Extendedsolversteps:5Totalsolveriterations:64ModelClass:NLPTotalvariables:4Nonlinearvariables:3Integervariables:0Totalconstraints:2Nonlinearconstraints:1Totalnonzeros:4Nonl
3、inearnonzeros:3VariableValueReducedCostB57.332090.000000C-0.4460386E-010.3922619E-07A2.4301770.000000X(1)2.0000000.000000X(2)5.0000000.000000X(3)7.0000000.000000X(4)10.000000.000000X(5)14.000000.000000X(6)19.000000.000000X(7)26.000000.000000X(8)31.00000
4、0.000000X(9)34.000000.000000X(10)38.000000.000000X(11)45.000000.000000X(12)52.000000.000000X(13)53.000000.000000X(14)60.000000.000000X(15)65.000000.000000Y(1)54.000000.000000Y(2)50.000000.000000Y(3)45.000000.000000Y(4)37.000000.000000Y(5)35.000000.00000
5、0Y(6)25.000000.000000Y(7)20.000000.000000Y(8)16.000000.000000Y(9)18.000000.000000Y(10)13.000000.000000Y(11)8.0000000.000000Y(12)11.000000.000000Y(13)8.0000000.000000Y(14)4.0000000.000000Y(15)6.0000000.000000RowSlackorSurplusDualPrice144.78049-1.000000即a
6、=2.4302,b=57.3321,c=-0.0446039y=2.4302+57.3321e^(-0.0446039x)η=2.4302+57.3321e-0.0446039ξ（2）最小一乘法，分别用x、y代替ξ、η的形式时的lingo程序：sets:quantity/1..15/:x,y;endsetsdata:x=2,5,7,10,14,19,26,31,34,38,45,52,53,60,65;y=54,50,45,37,35,25,20,16,18,13,8,11,8,4,6;enddata
7、min=@sum(quantity:@abs(a+b*@exp(c*x)-y));@free(a);@free(b);@free(c);运行程序后可得：Linearizationcomponentsadded:Constraints:60Variables:60Integers:15Localoptimalsolutionfound.Objectivevalue:20.80640Objectivebound:20.80640Infeasibilities:0.1219750E-06Extendedso
8、lversteps:0Totalsolveriterations:69ModelClass:MINLPTotalvariables:64Nonlinearvariables:2Integervariables:15Totalconstraints:62Nonlinearconstraints:15Totalnonzeros:196Nonlinearnonzeros:30VariableValueReducedCostA3.3982660.000000B5
