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Nondifferentiable Optimization and
An Extension of the Method of Subgradients
Nonsmooth Optimization and Nonlinear
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algorithm Application Approximation assume Balinski bundle methods computing condition numbers Conjugate Subgradients constrained least squares constraints Convergence Rate Convex Functions Cybernetics defined Demjanov denote descent direction Descent Method differentiable directional derivative Doklady Ermolev execution of Step exists extremal-value function f(xk feasible finite function f given gk+1 Gradient Method holds IIASA iteration Kibern Kibernetika Lagrange multipliers least squares problem Lemarechal Lemma lim inf line-search linear programming Lipschitz Lipschitz Continuous Mathematical Programming matrix Method for Solving Mifflin Minimax Minimization Method Moscow Nauk Nauka Nondifferentiable Functions Nondifferentiable Optimization Nonlinear Programming Nonsmooth Optimization Nurminskii Operations Research P(xk Poljak Programming Problems Proof Pshenichnyi quasidifferentiable rate of convergence relaxation method result Russian satisfied semismooth sequence SIAM Journal solution Soviet Math Space Dilation Stochastic Programming subgradient method subgradient optimization Suppose Systems tion variables vector Wolfe x e P(y,z xk+1 Yu.M