How can I find &#x03BB;<!-- λ --> H </msub> and &#x03BB;<!-- λ -->

Laila Andrews 2022-05-09 Answered
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 } < 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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Answers (1)

notemilyu1208
Answered 2022-05-10 Author has 14 answers
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 < 1. Is it a constraint? If so it should be written as a constraint.

If you want to impose the value is < 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.
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