最大最小对偶.ppt

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1、最大最小对偶 Still waters run deep.流静水深流静水深,人静心深人静心深 Where there is life, there is hope。有生命必有希望。有生命必有希望x Xy YF x yminmax( , ) F x yxX yY( , ),x Xy YF x ymaxmin( , ) x Xy YF x yF x yF x yxX yY1)min( , )( , )max( , ), x Xx Xy Yy YF x yF x y2)maxmin( , )minmax( , ) x Xx Xy Yy YgapF x yF x y3)minmax( , )maxmi

2、n( , )min maxinfsup2x Xy YF x yminmax( , )2 xXyY1,2 ,1,2 ,x Xy YF x ymaxmin( , )2 xyF x ya( , ), ijAa12()43 gap0 ijAa12()41 x Xy YF x yminmax( , )2 x Xy YF x ymaxmin( , )1 gap10 3( , ),F x yxX yYx Xy YF x yF x yF x yxX yY1)min( , )( , )max( , ), x Xx Xy Yy YF x yF x y2)maxmin( , )minmax( , ) x Xx Xy

3、 Yy YgapF x yF x y3)minmax( , )maxmin( , )*,xX yYF xyF xyF x yxX yY*(, )(,)( ,), x Xx Xy Yy YF x yF x y4)minmax( , )maxmin( , ) xy*(,)4f xs tg(x)h xmin ( ). . 0, ( )0 TTL x u vf xu g xv h xu( , , )( )( )( )(0) nTTx Ru vf xu g xv h xu ( , )min( )( )( ) ,0 其其中中nnuvuvuvx Rx RL x u vu vL x u v 0,0,0,2)m

4、axmin ( , , )max ( , )minmax ( , , )nuvx Rf xxSL x u vL x u vf xL x u vxS0,( ),min ( , , )( , , )( )max ( , , ), xS uv1),0, , nnuvuvx Rx RL x u vL x u v0,0,3)minmax ( , , )maxmin ( , , ) 原规划原规划uvu v 0,max ( , ) 凹函数凹函数5xs tx2min . . 10 20,2min . . 10 xxs tx nnuvuvx Rx RL x u vL x u v0,0,minmax ( , ,

5、)maxmin ( , , ) xxs txxxx22121212min . . 40,0 xxs txxxx121212min -2. . 30(,)(0,0),(0,4),(4,4),(4,0),(1,2),(2,1) 22121212min . . 40,0 xxs txxxx 6像集像集722121211min. .40,0 xxs txxx x2( )4 ,02uuu u 89f xs tg(x)h xmin ( ). . 0, ( )0 x,u v10f xs tg(x)h xmin ( ). . 0, ( )0 TTL x u vf xu g xv h xu( , , )( )(

6、 )( )(0)x u vxL x u vs tL x u vu, ,max ( , , ). . ( , , )0,0. 111min2. .0nTTx Rx Qxc xs tAxd1min2. .00nTTx Rx Qxc xs tAxbCxd1min2. .00nTTx Rx Qxc xs tAxbCxdlxu1min2. .0nTTTx Rx HH xc xs txC,1min2. .,0nTTx RyTy yc xs tyH xxC1max2Tuu uC Huc12共轭对偶、广义共轭对偶、广义Lagrange对偶对偶参阅参阅非线性规划及其理论非线性规划及其理论第第6章章应玖茜、魏权龄应玖茜、魏权龄13