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An algorithm for nonsmooth convex minimization with errors


Author: Krzysztof C. Kiwiel
Journal: Math. Comp. 45 (1985), 173-180
MSC: Primary 90C25; Secondary 65K05
DOI: https://doi.org/10.1090/S0025-5718-1985-0790650-5
MathSciNet review: 790650
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Abstract: A readily implementable algorithm is given for minimizing any convex, not necessarily differentiable, function f of several variables. At each iteration the method requires only one approximate evaluation of f and its $ \varepsilon $-subgradient, and finds a search direction by solving a small quadratic programming problem. The algorithm generates a minimizing sequence of points, which converges to a solution whenever f has any minimizers.


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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1985-0790650-5
Keywords: Mathematical programming, nonsmooth optimization, convex nondifferentiable optimization, descent methods, aggregate subgradients
Article copyright: © Copyright 1985 American Mathematical Society

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