I`m trying to solve a maximization problem: max p w ln ( ∑ i = 1 I p i a i ) − ∑ i = 1 I p i d i ,where p i ∈ { 0 , 1 } is binary variable and ∑ i = 1 I p i = 1. I need to find optimal p i ∗ , where p ∗ = arg ⁡ max p w ln ( ∑ i = 1 I p i a i ) − ∑ i = 1 I p i d i Is there any way to obtain the closed-form of p i ∗ as the function of w, a i , and d i ?

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I`m trying to solve a maximization problem:      max                  p              w  ln            (            ∑          i      =      1        I        p    i        a    i              )        −      ∑          i      =      1              I            p    i        d    i    ,where       p    i    ∈  {  0  ,  1  } is binary variable and       ∑          i      =      1        I        p    i    =  1. I need to find optimal       p    i    ∗  , where            p        ∗    =  arg  ⁡      max                  p              w  ln            (            ∑          i      =      1        I        p    i        a    i              )        −      ∑          i      =      1              I            p    i        d    i  Is there any way to obtain the closed-form of       p    i    ∗   as the function of   w,       a    i  , and       d    i  ?

Giovanna Erickson · Accepted Answer

It is just       p    i    =  [  i  =      i    ∗    ], where       i    ∗    =  arg  ⁡      max    i    (  w  ln  ⁡      a    i    −      d    i    ). The square brackets here are Iverson notation.

I`m trying to solve a maximization problem: <munder> <mo movablelimits="true" form="pref

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