期刊
COMPUTATIONAL OPTIMIZATION AND APPLICATIONS
卷 71, 期 2, 页码 381-402出版社
SPRINGER
DOI: 10.1007/s10589-018-0009-z
关键词
Market equilibrium; Smooth homotopy; Minimax problem; Regularization technique
资金
- Hong Kong SAR Government [GRF: CityU 11301014]
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(l){f(l)(x)} with f(l)(x) being a smooth concave function for all 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.
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