Theory and Applications of D-Gradients

Theoretical and applied aspects of a qualitatively new approach to operations with mathematical objects associated with systems of functions are developed. The basis for the built differential-geometry constructions is actions with d-gradients. The obtained results allowed to reveal the detailed picture of the inclusion for manifolds with broken boundary; deduce simple and explicit formulas for admissible directions and curves of the greatest function descent for optimization problems with constraints; establish a class of d-norms whose spherical surfaces have breaks identical to those of the constraints; construct algorithms for solutions to inequalities; create numerical d-gradient methods of minimization whose virtue consists in multiple gains in computations.