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Grad Student Seminar: Yang Zhan

June 15, 2018 @ 3:30 pm - 4:30 pm

The Department of

Statistics and Operations Research

The University of North Carolina at Chapel Hill


Summer

Graduate Seminar

Friday, June 15, 2018

120 Hanes Hall

3:30pm


Yang Zhan

Department of Systems Engineering and Engineering Management, 
City University of Hong Kong

 

Computing market equilibria under a class of

piecewise-smooth concave utilities

 

Computing a market equilibrium in general cases remains to be a very challenging problem. In the literature, there have been developed several dedicated algorithms for nondifferentiable utilities, such as Leontief and separable piecewise-linear utilities. But most of these methods require all consumers to have the same type of preferences. Using homotopy method, we develop a path-following algorithm for an 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. Based on a new regularization 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. An approximated solution can be obtained at the end of the path.

 

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Details

Date:
June 15, 2018
Time:
3:30 pm - 4:30 pm

Venue

Hanes 120