Continuous algorithms for solution of convex optimization problems and finding saddle points of contex-coneave functions with the use of projection operations

Continuous algorithms are proposed and studied for solution of convex programming problems and for finding the saddle points of convex-concave functions by the use of projection. The theory of monotone operators, convex analysis, and the direct Lyapukov method are employed to establish the existence, uniqueness, and infinite extendibility of solution to differential equation systems with a discontinuous right-hand side that represent the algorithms. The asymptotic properties of these systems are studied.