318 Hanes Hall, CB #3260 Chapel Hill, NC 27599-3260
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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


Graduate Seminar

Friday, June 15, 2018

120 Hanes Hall


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


Hanes 120