A smooth path-following algorithm for market equilibrium under a class of piecewise-smooth concave utilities

Yang Zhan () and Chuangyin Dang ()
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Yang Zhan: City University of Hong Kong
Chuangyin Dang: City University of Hong Kong

Computational Optimization and Applications, 2018, vol. 71, issue 2, No 4, 402 pages

Abstract: Abstract This paper presents a smooth path-following algorithm for computing market equilibrium in a pure exchange economy under a class of piecewise-smooth concave utilities, which can be expressed as $$u(x)=\min _\ell \{f_\ell (x)\}$$ u ( x ) = min ℓ { f ℓ ( x ) } with $$f_\ell (x)$$ f ℓ ( x ) being a smooth concave function for all $$\ell $$ ℓ . As a result of a smooth technique for minimax problems, a smooth homotopy mapping is derived from the introduction of logarithmic barrier terms and an extra variable. With this mapping, it is proved that there always exists a smooth path leading to a market equilibrium as the extra variable approaches zero. A predictor–corrector method is adapted for numerically following this path. Numerical results are given to further demonstrate the effectiveness and efficiency of the algorithm.

Keywords: Market equilibrium; Smooth homotopy; Minimax problem; Regularization technique (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (5)

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DOI: 10.1007/s10589-018-0009-z

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