h://jnrm.rbau.ac.r پژوهشهای نوین در ریاضی دانشگاه آزاد اسالمی واحد علوم و تحقیقات * Correondng auhor, Emal: j.val@abrzu.ac.r. *
تخمین
x x x, c x e d.. A x B b.. A x B b, 2 2 2 A d,, e n2 cx, n A 2 mn2 m2n2 B B 2 m n m2n x, c x d.. A x B b e.. A x B b 2 2 2 ( x, ) x A x B b.
Y X E { x X x X; Cx Cx, Cx Cx} Y { Cx x X E }. Cx Cx Cx xx X WE xx x mn cx mn cx 2 mn cx.. Ax b x 0, Y W b m x n A mn c, c2,, c n XWE { xx xx; Cx Cx} Y { Cx xx }. W WE. Y YW XEXWE n X{ x Axb, x0} c x C Y{ Cxx X} xx Y xx.. Y 0, Cx Cx, Cx Cx Cx X E x
.. Y,2,, 2 I mn.. Y Y.. 0, Y I,, 2,, Y I mn.. Y I ( I, I,, I 2 ),2,, (,,, 2 )
M, c.. Y M.. Y 0 Y (, ) z.. c Y z c M 2,.. Y.. Y 0 c.. Y Y Y 0
c.. Y W Y Y YW YW ( *, 0) * Y * * M z ( *, 0) * c. 2 c M (),.. Y.. Y 0 ( *, 0) z z z 2 2 ( * *, 0) z2z ( *, *) * 0 * Y * * (, ) * 0 M z ( * *, ) ( * 0, *), z 2 2 * * (, ) e c ( ) ce Y z2z * ( *, 0) * * * ( *, ) ( * c 0 ). z z z z 2 2 z2z
v ( v C w A) x 0 ( v ) 0 ( Ax) 0 w b x 0, 0, w 0 x,, x, x, M.. Cx Ax b x 0.. Cx Ax b x 0, 0 K 0,,( ) 0 v C w A 0 x 0 v C w A x v, 0, ( v ) 0 w 0 Ax b w b Ax,, ( ) 0 0 v C w A, 0 x ( ), K K n {0,}, j,2,, n j 0 v q, 0 ( q), K K q {0,},,2,, 0 w K, 0 b Ax K( m ), {0,},,2,, m KKT 0 M x,, x,.. Cx Ax b x 0 Cx Ax b v C w A 0
x x2 x3 x4 x5 x6 x7 x, x2, x3, x4, x5, x6, x70 -x2 x3 2x49x5 9x69x7 2 -x x3 9x4 2x5 9x69x7 2 3 -x x2 9x49x5 2x62x7 3 x x2 x3 x4 x5 x6x7 0 v 2v 3 w K 0v v3 w K 2 0v v 2 w K 3 02v 9v 29v 3 w K 4 09v 2v 29v 3 w K 5 09v 9v 22v 3 w K 6 09v 9v 22v 3 w K 7 v, v 2, v 3 0 x K ( ) 0 x2k ( 2) 0 x3 K ( 3) 0 x4k ( 4) 0x5 K ( 5) 0 x6k ( 6) 0 x7k ( 7), 2, 3, 4, 5, 6, 7{0,}. Mn -x 2 -x3-2x 4-9x5-9x6 + 9x 7 Mn -x -x 3-9x 4-2x5-9x6 +9x7 Mn - - -9-9 - -2 x x x x 2x x 2 4 5 6 7.. x x 2 + x3 + x 4 + x5 + x6 + x7 = x, x 2, x3, x 4, x5, x6, x7 0 (0, 0, 0). Max -M( + 2+ 3).. = -x2-x3-2x4-9x5-9x6+ 9x7 2 = -x -x3-9x4-2x5-9x6+9x7 3 = -x-x2-9x4-9x5-2x6-2x7 + + + + + + = x x x x x x x 2 3 4 5 6 7 x, x2, x3, x4, x5, x6, x70 Max + + 2 3.. = -x2 -x3-2x4-9x5-9x6+ 9x7 2 2= -x -x3-9x4-2x5-9x6 +9x7 3 3= -x -x2-9x4-9x5-2x6-2x7 x + x2 + x3 + x4 + x5 + x6 + x7 = x, x2, x3, x4, x5, x6, x7 0 K Max.. -x2x32x49x59x69x7 2 -x x39x42x59x69x7 3 -x x2 9x49x52x62x7
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