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  • 8/11/2019 Multivariable Problem With Equality Constraints

    1/20

    : ..

  • 8/11/2019 Multivariable Problem With Equality Constraints

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    , 602:

    /

    = 0 = 1,2,3, ,

    = , , , ,

    = 0

  • 8/11/2019 Multivariable Problem With Equality Constraints

    3/20

    , 602:

    , /

    , = 0

    , = 0

    ,

    = + = 0

    ,

    , ,

    , = 0

    + , + = 0

  • 8/11/2019 Multivariable Problem With Equality Constraints

    4/20

    , 602:

    , /

    , = 0

    , = 0

    ,

    + , + = 0

    + , + = , + , + ,

    =0

    = + = 0

    =

  • 8/11/2019 Multivariable Problem With Equality Constraints

    5/20

    , 602:

    , /

    , = 0

    , = 0

    ,

    =

    = +

    = 0

    =

    = 0

    = 0

    = 0

  • 8/11/2019 Multivariable Problem With Equality Constraints

    6/20

  • 8/11/2019 Multivariable Problem With Equality Constraints

    7/20

    , 602:

    , , = , + ,

    ,

    = + = 0

    = +

    = 0

    = , = 0

  • 8/11/2019 Multivariable Problem With Equality Constraints

    8/20

    , 602:

    , , = , + ,

    =

    =

    0

    ,

    ,

  • 8/11/2019 Multivariable Problem With Equality Constraints

    9/20

    , 602:

    /

    = 0 = 1,2,3, ,

    = , , , ,

    , , , , , , , = + + , ,

    =

    +

    = 0

    = = 0

  • 8/11/2019 Multivariable Problem With Equality Constraints

    10/20

    , 602:

    =

    0

    0 0

    0 0

    0

    ,

  • 8/11/2019 Multivariable Problem With Equality Constraints

    11/20

    , 602:

    /

    = , = 0

    = 0

    = , , , ,

    , = 1,2,3, ,

    = 0

    = 0

    = =

    =

    = 1

    =

    =

    =

    T T T T

    > 0< 0= 0

  • 8/11/2019 Multivariable Problem With Equality Constraints

    12/20

    , 602:

    0 = 1,2,3, ,

    = , , , ,

    + = 0

    , = +

    = 0 = 1,2,3, ,

    = , , , ,

  • 8/11/2019 Multivariable Problem With Equality Constraints

    13/20

    , 602:

    , = + = 0 = 1,2,3, ,

    = , , , ,

    , , = + ,

    ,, =

    +

    = 0

    ,,

    = , = + = 0

    = 1,2,3, ,

    = 1,2,3, , ,,

    20 = 1,2,3, ,

  • 8/11/2019 Multivariable Problem With Equality Constraints

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    , 602:

    ,, 20

    0 , 0

    0, ,

    0, , , ,

    +

    = 0 = 1,2,3, ,

    = 0 + = 0

  • 8/11/2019 Multivariable Problem With Equality Constraints

    15/20

    , 602:

    = +

    +

    + +

    = 1,2,3, ,

    = + + + + =

    =

    .

    = + ,

    =

    +

    < 0 < 0

    , > 0 +

    , > 0,

  • 8/11/2019 Multivariable Problem With Equality Constraints

    16/20

    , 602:

    = 0

    = 0

    < 0 < 0

    > 0

    > 0

  • 8/11/2019 Multivariable Problem With Equality Constraints

    17/20

    , 602:

    +

    = 0 = 1,2,3, , 0

    . ,

    , ,

    .

  • 8/11/2019 Multivariable Problem With Equality Constraints

    18/20

    , 602:

    ,

    +

    = 0 = 1,2,3, ,

    = 0

    0 0 = 1,2,3, ,

  • 8/11/2019 Multivariable Problem With Equality Constraints

    19/20

    , 602:

    +

    +

    = 0 = 1,2,3, ,

    = 0

    0

    0

    = 1,2,3, ,

    = 0 = 1,2,3, ,

    = , , , ,

    = 0 = 1,2,3, ,

    = 1,2,3, , = 0 = 1,2,3, , = 1,2,3,,

  • 8/11/2019 Multivariable Problem With Equality Constraints

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    , 602:


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