matlab优化函数的使用方法.docVIP

三． 举例 例1：求解线性规划问题： ??????????????max f=2x1+5x2 ??????????????s.t 先将目标函数转化成最小值问题：min(-f)=- 2x1-5x2 程序： f=[-2 -5]; A=[1 0;0 1;1 2]; b=[4;3;8]; [x,fval]=linprog(f,A,b) f=fval*(-1) 结果：?? x = 2?? 3 ???????????????????? fval = -19.0000 maxf =??19 例2：minf=5x1-x2+2x3+3x4-8x5 s.t??–2x1+x2-x3+x4-3x5≤6 ????2x1+x2-x3+4x4+x5≤7 ????0≤xj≤15??j=1,2,3,4,5 程序： f=[5 -1 2 3 -8]; A=[-2 1 -1 1 -3;2 1 -1 4 1]; b=[6;7]; lb=[0 0 0 0 0]; ub=[15 15 15 15 15]; [x,fval]=linprog(f,A,b,[],[],lb,ub) 结果：x = ?????????? 0.0000 ?????????? 0.0000 ?????????? 8.0000 ?????????? 0.0000 ????????????15.0000 minf = ??-104 例3：求解线性规划问题： ???????????????????? minf=5x1+x2+2x3+3x4+x5 s.t??–2x1+x2-x3+x4-3x5≤1 ????????????????2x1+3x2-x3+2x4+x5≤-2 ????????????????????0≤xj≤1??j=1,2,3,4,5 程序： ?????? f=[5 1 2 3 1]; ?????? A=[-2 1 -1 1 -3;2 3 -1 2 1]; ?????? b=[1;-2]; ?????? lb=[0 0 0 0 0]; ?????? ub=[1 1 1 1 1]; ?????? [x,fval,exitflag,output,lambda]=linprog(f,A,b,[],[],lb,ub)?????????????????????????? 运行结果：???????? ?????? Exiting: One or more of the residuals, duality gap, or total relative error ???????? has grown 100000 times greater than its minimum value so far: ???????? the primal appears to be infeasible (and the dual unbounded). ???????? (The dual residual TolFun=1.00e-008.) x = 0.0000 ?????????????????? 0.0000 ?????????????????? 1.1987 ?????????????????? 0.0000 ????????????????????0.0000 fval = ??????????????????2.3975 exitflag = ??????????????????-1 output = ??????????iterations: 7 ?????????? cgiterations: 0 ???????? algorithm: lipsol lambda = ??????????????????ineqlin: [2x1 double] ???????????????? eqlin: [0x1 double] ???????????????? upper: [5x1 double] ???????????????? lower: [5x1 double] ?????? 显示的信息表明该问题无可行解。所给出的是对约束破坏最小的解。 ?????? 例4：求解实例1的生产计划问题 建立数学模型： 设x1、x2分别为生产甲、乙产品的件数。f为该厂所获总润。 ?????? max f=70x1+120x2 ?????? s.t??9x1+4x2≤3600 ????????4x1+5x2≤2000 ????????3x1+10x2≤3000 ????????x1,x2≥0 将其转换为标准形式： min f=-70x1-120x2 ?????? s.t??9x1+4x2≤3600 ????????4x1+5x2≤2000 ????????