Invariant Straightening of Foliations and a Theory of Direct Methods for Constrained Optimization

Mathematical apparatus of the bent-straightened problems of constrained optimization is developed. Basing on this a united theory of the computational schemes of the direct methods for minimization is derived. Using this theory existing methods are reconstructed as well as qualitatively new promising computational schemes are obtained. In so doing essential alterations to some known methods are made which results in ridding them of substantial mistakes.