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A.I. Propoi algorithm applied Automation and Remote ber of Final chapter Chem computations concave concave function condition constraints convergence convex set criterion value D.P. Bertsekas define definition of Hamiltonian directional convexity Discrete Maximum Principle Discrete Systems discrete time systems dynamic programming equation examples formulated Gabasov given H.F. Ravn Halkin higher loop IMSOR inf ub(x J.M. Holtzman JOTA L.S. Pontryagin Lagrange Multiplier Method linear support loop step maximizes the Hamiltonian Multiplier Method multistage optimization problems n-dimensional Nauk SSSR nonlinear programming Optimal Control Optimal Processes optimal solution Optimal values optimization of discrete penalty functions Pontryagin's Maximum Principle Principle for Discrete quadratic support ri(xi'ui Russian saddle-point sequence shadow price situated at ub strong support support to ub(x Theorem 222 Theorem ll6 Theory of Optimal ti(x tion UBjxJ UBN(xN upper boundary approach variables vector Vidal xi+1 xi+rxi