Refined theorems on the relaxation of equality constraints in an optimal control problem, linear with respect to the control (Q923353)

Necessary conditions for the possibility of transforming an optimization problem with singular (in terms of first and second order expansions in the neighbourhood of 0) equality constraints, to an equivalent problem with inequality constraints are proved. These conditions are finer than the ones proposed by the author previously [see Math. USSR, Izv. 31, No.1, 121-141 (1988); translation from Izv. Akad. Nauk SSSR, Ser. Mat. 51, No.4, 812-832 (1987; Zbl 0679.49025)].