Concave/Convex Function rate of increase

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I have the following constraints:
$$sum_i=1^2 p_i =2P$$
$$sum_i=1^2 gamma_i =2Gamma$$
and the function $R$ which is strictly concave w.r.t. $p$ and strictly convex w.r.t. $gamma$. How do I prove the following:
$$2R(P,Gamma) geq sum_i=1^2 R(p_i, gamma_i) $$




summation convex-analysis constraints




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    up vote
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    down vote

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    I have the following constraints:
    $$sum_i=1^2 p_i =2P$$
    $$sum_i=1^2 gamma_i =2Gamma$$
    and the function $R$ which is strictly concave w.r.t. $p$ and strictly convex w.r.t. $gamma$. How do I prove the following:
    $$2R(P,Gamma) geq sum_i=1^2 R(p_i, gamma_i) $$




    summation convex-analysis constraints




    share|cite|improve this question





















      up vote
      0
      down vote

      favorite









      up vote
      0
      down vote

      favorite











      I have the following constraints:
      $$sum_i=1^2 p_i =2P$$
      $$sum_i=1^2 gamma_i =2Gamma$$
      and the function $R$ which is strictly concave w.r.t. $p$ and strictly convex w.r.t. $gamma$. How do I prove the following:
      $$2R(P,Gamma) geq sum_i=1^2 R(p_i, gamma_i) $$




      summation convex-analysis constraints




      share|cite|improve this question











      I have the following constraints:
      $$sum_i=1^2 p_i =2P$$
      $$sum_i=1^2 gamma_i =2Gamma$$
      and the function $R$ which is strictly concave w.r.t. $p$ and strictly convex w.r.t. $gamma$. How do I prove the following:
      $$2R(P,Gamma) geq sum_i=1^2 R(p_i, gamma_i) $$





      summation convex-analysis constraints





      share|cite|improve this question










      share|cite|improve this question




      share|cite|improve this question









      asked Jul 23 at 11:04









      Miroslav

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