nlsq solver with linear (bound) constraints generates out of boundary guesses

[Nikolay_P_1]

Hello everybody,

This is my second post with a set of questions about using the nonlinear least square solver from mkl (the first one is about the OMP parallelization is here   http://software.intel.com/en-us/forums/topic/495859 )

I implemented this algorithm following the example in the mkl

unfortunately the solver keeps escaping the region set by UP and LW http://software.intel.com/sites/products/documentation/hpc/mkl/mklman/GUID-B6BADF1C-F90C-4D30-8B84-CF9A5F970E08.htm#GUID-B6BADF1C-F90C-4D30-8B84-CF9A5F970E08

where I really don't want it to go (because my function misbehaves there) 

I first thought it is the rs parameter (which I assume to be the max s in s*J, but I'm not sure from the given explanation) and in the example provided by intel it is misleadingly initialized to 0.0 while it has to be between 0.1 and 100(default). Anyway, I had it default 100, then put it to 10.0; 1.0 and 0.1, changed iter2 from 100 to 10 and to 1 (to prevent it from extrapolating too far with the first step derivatives) but it runs away again at the second step to the same numbers no matter what I do!

sending to the solver at initialization:

x0(1) -47.270320 LW(1) -56.724384 UP(1) -37.816256

x0(2) -36.266918 LW(2) -43.520302 UP(2) -29.013534

guess solutions sent by the solver to my function (from the function)

thread 0
x0(1)          -47.270320                                x_step2(1)   -70.905480
x0(2)          -36.266918                                x_step2(2)  -36.266918

thread 1
x0(1)          -47.270320                                x_step2(1) -47.270320
x0(2)          -36.266918                                x_step2(2) -18.133459

This is what I am sending to the solver at initialization (which reports success)

initialize solver (allocate mamory, set initial values)
                 n1      in:     number of refined parameters 15
                 m1      in:     1D function value F 16800
                 iter1   in:      maximum number of iterations 100
                 iter2   in:       maximum number  of trial-steps 1
                 rs      in:       initial step bound 0.100000
                 SUCCESS

Did anybody have the same troubles? Anybody can give me any pointers?

[mecej4]

Many algorithms for nonlinear constrained optimization do not restrict requests for function and constraint evaluations to points only within the feasible region. In fact, the initial step in some algorithms is to find a feasible point, from whence a path can be followed along which the objective function decreases.

Search the Web for FSQP and CFSQP -- these were software packages which searched for an optimum while staying within the feasible region.