Author | Shor, Naum Zuselevich. author |
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Title | Minimization Methods for Non-Differentiable Functions [electronic resource] / by Naum Zuselevich Shor |
Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg, 1985 |
Connect to | http://dx.doi.org/10.1007/978-3-642-82118-9 |
Descript | VIII, 164 p. online resource |
1. Special Classes of Nondifferentiable Functions and Generalizations of the Concept of the Gradient -- 1.1 The Need to Introduce Special Classes of Nondifferentiable Functions -- 1.2 Convex Functions. The Concept of Subgradient -- 1.3 Some Methods for Computing Subgradients -- 1.4 Almost Differentiable Functions -- 1.5 Semismooth and Semiconvex Functions -- 2. The Subgradient Method -- 2.1 The Problem of Stepsize Selection in the Subgradient Method -- 2.2 Basic Convergence Results for the Subgradient Method -- 2.3 On the Linear Rate of Convergence of the Subgradient Method -- 2.4 The Subgradient Method and Fejer-type Approximations -- 2.5 Methods of ?-subgradients -- 2.6 An Extension of the Subgradient Method to a Class of Nonconvex Functions. Stochastic Versions and Stability of the Method -- 3. Gradient-type Methods with Space Dilation -- 3.1 Heuristics of Methods with Space Dilation -- 3.2 Operators of Space Dilation -- 3.3 The Subgradient Method with Space Dilation in the Direction of the Gradient -- 3.4 Convergence of Algorithms with Space Dilation -- 3.5 Application of the Subgradient Method with Space Dilation to the Solution of Systems of Nonlinear Equations -- 3.6 A Minimization Method Using the Operation of Space Dilation in the Direction of the Difference of Two Successive Almost-Gradients -- 3.7 Convergence of a Version of the r-Algorithm with Exact Directional Minimization -- 3.8 Relations between SDG Algorithms and Algorithms of Successive Sections -- 3.9 Computational Modifications of Subgradient Methods with Space Dilation -- 4. Applications of Methods for Nonsmooth Optimization to the Solution of Mathematical Programming Problems -- 4.1 Application of Subgradient Algorithms in Decomposition Methods -- 4.2 An Iterative Method for Solving Linear Programming Problems of Special Structure -- 4.3 The Solution of Distribution Problems by the Subgradient Method -- 4.4 Experience in Solving Production-Transportation Problems by Subgradient Algorithms with Space Dilation -- 4.5 Application of r-Algorithms to Nonlinear Minimax Problems -- 4.6 Application of Methods for Minimizing Nonsmooth Functions to Problems of Interpreting Gravimetric Observations -- 4.7 Other Areas of Applications of Generalized Gradient Methods -- Concluding Remarks -- References