Characterizing Shadow Price via Lagrange Multiplier for Nonsmooth Problem

doi:10.1007/s40305-022-00416-6

Journal of the Operations Research Society of China ›› 2023, Vol. 11 ›› Issue (4): 827-838.doi: 10.1007/s40305-022-00416-6

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Characterizing Shadow Price via Lagrange Multiplier for Nonsmooth Problem

Yan Gao

School of Management, University of Shanghai for Science and Technology, Shanghai, 200093, China

Received:2021-05-22 Revised:2022-03-02 Online:2023-12-30 Published:2023-12-26
Contact: Yan Gao E-mail:gaoyan@usst.edu.cn
Supported by:
This work is supported by the National Natural Science Foundation of China (No. 72071130).

Abstract

Abstract: In this paper, the relation between the shadow price and the Lagrange multiplier for nonsmooth optimization problem is explored. It is obtained that the Lagrange multipliers are upper bounds of the shadow price for a convex optimization problem and a class of Lipschtzian optimization problems. This result can be used in pricing mechanisms for nonsmooth situation. Several nonsmooth functions involved in this class of Lipschtzian optimizations are listed. Finally, an application to electricity pricing is discussed.

Key words: Shadow price, Lagrange multiplier, Nonsmooth optimization

CLC Number:

49J52
91B24

Yan Gao. Characterizing Shadow Price via Lagrange Multiplier for Nonsmooth Problem[J]. Journal of the Operations Research Society of China, 2023, 11(4): 827-838.

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Characterizing Shadow Price via Lagrange Multiplier for Nonsmooth Problem

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