Frame-Based Ray Search Algorithms in Unconstrained Optimization

C.J. Price and I.D. Coope
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C.J. Price: University of Canterbury
I.D. Coope: University of Canterbury

Journal of Optimization Theory and Applications, 2003, vol. 116, issue 2, No 8, 359-377

Abstract: Abstract This paper describes a class of frame-based direct search methods for unconstrained optimization without derivatives. A template for convergent direct search methods is developed, some requiring only the relative ordering of function values. At each iteration, the template considers a number of search steps which form a positive basis and conducts a ray search along a step giving adequate decrease. Various ray search strategies are possible, including discrete equivalents of the Goldstein–Armijo and one-sided Wolfe–Powell ray searches. Convergence is shown under mild conditions which allow successive frames to be rotated, translated, and scaled relative to one another.

Keywords: Derivative-free optimization; positive basis methods; convergence analysis; frame-based methods; ray search (search for similar items in EconPapers)
Date: 2003
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DOI: 10.1023/A:1022414105888

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