On a space extension algorithm for nondifferentiable optimization |
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Authors: | M Z Yakin |
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Institution: | (1) Department of Quantitative Management Science, College of Business Administration, University of Houston, Houston, Texas |
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Abstract: | This paper presents a version of an algorithm, due to Shor, for solving unconstrained nondifferentiable optimization problems. The algorithm uses a space extension operator in the direction of the difference between two successive subgradients. The search direction is determined by multiplying the negative of a subgradient by a positive-definite and symmetric matrix. This matrix is updated by a formula similar to the DFP updating formula for differentiable problems. An approximate line search due to Wolfe is presented. A linear rate of convergence of the successive function values is established. |
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Keywords: | Nondifferentiable optimization space extension algorithm rate of convergence analysis strongly convex functions |
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