A deformational method of studying nonlinear programming problems. I

A new approach is proposed to analysis of extremals in nonlinear programming problems whereby the problem is deformed into a simpler analyzable problem. The basic result of the research is a deformational principle of the maximum: if in the course of deformation it stays isolated and minimizes the reference problem then the extremal can also minimize the problem at hand. Applications are indicated to analysis of singular extremals of optimization problems, problems in classical analysis, etc.