How can I find λ H and λ T such that max 0 ≤ λ H , λ T ≤ 1 { 4.6575342 × 10 − 4 2.1722965 × 10 − 4 + λ H , 1.0958904 × 10 − 2 3.4311896 × 10 − 4 + λ T } &lt; 1 ?Is this problem equivalent to finding x and y such that min 0 ≤ x , y ≤ 1 { .4664048 + ( 2147.0588450 ) x , 0.0313096 + ( 91.2500009 ) y } ≥ 1 ?

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How can I find       λ    H   and       λ    T   such that      max          0      ≤              λ        H            ,                     λ        T                   ≤      1            {                  4.6575342        ×                  10                      −            4                                      2.1722965        ×                  10                      −            4                          +                  λ          H                      ,                  1.0958904        ×                  10                      −            2                                      3.4311896        ×                  10                      −            4                          +                  λ          T                      }    &amp;lt;  1  ?Is this problem equivalent to finding   x and   y such that      min          0             ≤             x      ,             y                    ≤             1        {  .4664048  +  (  2147.0588450  )  x  ,  0.0313096  +  (  91.2500009  )  y  }  ≥  1  ?

notemilyu1208 · Accepted Answer

Each of the functions is convex, their max is then convex, so the solution of the maximization lies at one the corners: (0,0), (0,1), (1,0) and (1,1). It should be (0,0).What is not clear is the   &amp;lt;  1. Is it a constraint? If so it should be written as a constraint.If you want to impose the value is   &amp;lt;  1 then it is just a matter of increasing the variables from zero until the point you reach 1 or one of them hits one.

How can I find λ H </msub> and λ

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