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A general deterministic analysis to state the necessary conditions with acoefficient determination for the variational source condition to hold isprovided. Of particular interest in terms of the choice of the regularizationparameter, it is revealed that Morozov's discrepancy principle can be used bothfor determining new stable lower and upper bounds for the regularizationparameter. With these bounds, it is also possible to establish quantitativeestimations for the index function as well as for the different definitions ofthe Bregman distance. Inclusion of the variational source condition into thestability analysis enables one to re-establish convergence and convergence rateresults in terms of the index function. The coefficient in the variationalsource condition is explicitly defined as a multivariable function of constantsin Morozov's discrepancy principle. As expected, the results here areapplicable when any strictly convex, smooth/non-smooth objective functional isconsidered.

Generalized Variational Source Condition Associated with the Bregman  Distance-I: Verification of the Variational Source Condition and Stability of  the Total Error Estimation