Finding the minimum of a multivariate quartic function over a unit sphere.

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Finding the minimum of a quadratic function over a unit sphere is simple I believe. You just have to find the minimum eigenvalue of the coefficient matrix.



I would like to find the minimum of a multivariate quartic (4th order) function over a unit sphere. Is there a method for that? Numerical is also accepted.



It is actually related to the variance of an operator so there is the square of the expectation value which makes the function quartic.




polynomials quartic-equations




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    up vote
    0
    down vote

    favorite












    Finding the minimum of a quadratic function over a unit sphere is simple I believe. You just have to find the minimum eigenvalue of the coefficient matrix.



    I would like to find the minimum of a multivariate quartic (4th order) function over a unit sphere. Is there a method for that? Numerical is also accepted.



    It is actually related to the variance of an operator so there is the square of the expectation value which makes the function quartic.




    polynomials quartic-equations




    share|cite|improve this question





















      up vote
      0
      down vote

      favorite









      up vote
      0
      down vote

      favorite











      Finding the minimum of a quadratic function over a unit sphere is simple I believe. You just have to find the minimum eigenvalue of the coefficient matrix.



      I would like to find the minimum of a multivariate quartic (4th order) function over a unit sphere. Is there a method for that? Numerical is also accepted.



      It is actually related to the variance of an operator so there is the square of the expectation value which makes the function quartic.




      polynomials quartic-equations




      share|cite|improve this question











      Finding the minimum of a quadratic function over a unit sphere is simple I believe. You just have to find the minimum eigenvalue of the coefficient matrix.



      I would like to find the minimum of a multivariate quartic (4th order) function over a unit sphere. Is there a method for that? Numerical is also accepted.



      It is actually related to the variance of an operator so there is the square of the expectation value which makes the function quartic.





      polynomials quartic-equations





      share|cite|improve this question










      share|cite|improve this question




      share|cite|improve this question









      asked Aug 3 at 12:54









      Buddha_the_Scientist

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