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Math Help - nonconvex optimization

  1. #1
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    nonconvex optimization

    Hi,

    I've spent the last few months dealing with the following problem:

    min f(x)
    s.t. c_i(x)=0 i=1..m

    where x is in R^n, f(x) and c(x) are quadratic functions, having rank-deficient gradC(x) and gradF(x). I know that at least one solution exists.

    I've tried SQP, line search, trust region, incremental loading, pseudo arc-length continutation, augmented lagrangian.. all failed. Is it possible that my problem is that difficult and that there is no relevant literature on the topic?

    What I usually observe with SPQ-like methods, is that the constraints are violating very little (1e-14) at each iteration, but the residual of the first order optimality condition:

    R(x,s) = gradf(x) - s*gradC(x),

    where s are the Lagrange multipliers, never goes below 1e-7. Also, the solution x is very close to the starting guess, and the multipliers s are very high. And clearly x is not the minimizer I'm looking for.

    Thanks for the help,
    AQ
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  2. #2
    Super Member Rebesques's Avatar
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    I've tried SQP, line search, trust region, incremental loading, pseudo arc-length continutation, augmented lagrangian.. all failed.


    ...That's a sound way of knowing you are doing something interesting

    Now, the way you put it...

    I know that at least one solution exists.

    By what method? Maybe this will shed some light.
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  3. #3
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    thanks for the reply!

    this is kinda embarrassing but, well, we made a mistake and the system did not have a solution because the constraint and the energy gradient were exactly orthogonal.. something to remember next time before wasting all that time implementing those solvers!
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