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What does it mean that for epsilon constraint method, a pareto optimal $x^*$ would satisfy $epsilon = f(x^*)$?



The 2019 Stack Overflow Developer Survey Results Are InRelaxed optimization problemsEpsilon constraint method - Pareto optimal solution representationConvert optimization problem to series of equations to solve all variables in O(1)Is there a solution for problems with non-convex constraints?Optimize $beginalign min _ (x_1,..,x_n) sum_i=1^n sum_k=1^n e^-frac(x_i-x_k)^22 endalign$ such that $|x_i|le a$Convert NL equality constraint involving minimum to linear inequality constraint?What is the KKT condition for constraint $M preceq I$?Solving a LP problemWhat's the difference between optimal solutions, weakly Pareto and Pareto solutions?Optimization: Coupling Variables










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What does it mean that for epsilon constraint method, a pareto optimal $x^*$ would satisfy $epsilon = f(x^*)$?



The problem with this is that this seems like a different definition compared to the "dominating definition" for pareto optimal solution.



Say if the $epsilon = (0.0,0.1)$ and our problem would be $min (x_1,x_2^2), x_1,x_2 geq 0$. Then $f(0.0,0.0)=(0.0,0.0) not= (0.0,0.1)$










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    0












    $begingroup$


    What does it mean that for epsilon constraint method, a pareto optimal $x^*$ would satisfy $epsilon = f(x^*)$?



    The problem with this is that this seems like a different definition compared to the "dominating definition" for pareto optimal solution.



    Say if the $epsilon = (0.0,0.1)$ and our problem would be $min (x_1,x_2^2), x_1,x_2 geq 0$. Then $f(0.0,0.0)=(0.0,0.0) not= (0.0,0.1)$










    share|cite|improve this question









    $endgroup$














      0












      0








      0





      $begingroup$


      What does it mean that for epsilon constraint method, a pareto optimal $x^*$ would satisfy $epsilon = f(x^*)$?



      The problem with this is that this seems like a different definition compared to the "dominating definition" for pareto optimal solution.



      Say if the $epsilon = (0.0,0.1)$ and our problem would be $min (x_1,x_2^2), x_1,x_2 geq 0$. Then $f(0.0,0.0)=(0.0,0.0) not= (0.0,0.1)$










      share|cite|improve this question









      $endgroup$




      What does it mean that for epsilon constraint method, a pareto optimal $x^*$ would satisfy $epsilon = f(x^*)$?



      The problem with this is that this seems like a different definition compared to the "dominating definition" for pareto optimal solution.



      Say if the $epsilon = (0.0,0.1)$ and our problem would be $min (x_1,x_2^2), x_1,x_2 geq 0$. Then $f(0.0,0.0)=(0.0,0.0) not= (0.0,0.1)$







      optimization






      share|cite|improve this question













      share|cite|improve this question











      share|cite|improve this question




      share|cite|improve this question










      asked Apr 6 at 20:02









      mavaviljmavavilj

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      2,85711138




















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