Solving a Min-Max Optimization Problem with Constraint

Question

I'm trying to solve the following optimization problem:

min max{x + 2y − 1, 2x + 0.5y + 0.75} s.t. x + y = 1,

so far i've tried to solve it separately in terms of max and min but im not sure when i can use the constrain, can i solve it as : max{x + 2y − 1, 2x + 0.5y + 0.75} s.t x+y=1 and then taking the min value

or

finding the max value and then solve the problem under the constrain that x+y=1

Additionally, in the total case i would like to know if max min(f,g,...,h)) equals to any function.

Thank you.

Answer 1

I would interpret this, and formulate this as:

  min z
      z >= x + 2y − 1
      z >= 2x + 0.5y + 0.75
      x + y = 1 
      x,y >= 0 (???)