Suboptimal reconciliation

The goal of the suboptimal reconciliation is to find some z e 51/ (thus g(z) = 0) by a sequence of approximations such that the final subvector x of z is as close as possible to the measured x" , which is expressed by the adjustments (10.4.14), and we have also the subvector y, uniquely determined by X if observable, else not too distant from the initial guess y according to the condition (10.4.16), thus with successive corrections (10.4.17). We thus begin with... 

Thus we start our correction again in the direction w , but possibly with a shorter step. Using then again the suboptimal reconciliation starting from z " as the initial guess, we thus arrive at some z instead of z . We expect that if x is sufficiently small then... 

Suboptimal reconciliation according to Subsection 10.4.2, starting from... 

The above strategy, with possible x < 1 in (10.4.19 and 45), consists of approximating first the sought minimum by a point 2 M (suboptimal reconciliation) and then decreasing the criterion Q (10.4.32) by a series of steps subjected to the condition (10.4.46) where is the k-th value of the criterion. A simpler strategy as follows is, in fact, a version of succesive quadratic programming see Remark (i) below. 

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