Solution Path of the Perturbed Karush-Kuhn-Tucker System for Stochastic Nonlinear Programming with Inequality Constraints
Received:January 22, 2019  Revised:March 03, 2019
Key Word: Stochastic nonlinear programming   stability analysis   strong regularity   second order optimality conditions   constraint qualification  
Fund ProjectL:Supported by the National Natural Science Foundation of China (Grant Nos.11571059; 11731013).
Author NameAffiliation
Liwei ZHANG School of Mathematical Science, Dalian University of Technology, Liaoning 116024, P. R. China 
Shengzhe GAO School of Mathematical Science, Dalian University of Technology, Liaoning 116024, P. R. China 
Shaoyan GUO School of Mathematical Science, Dalian University of Technology, Liaoning 116024, P. R. China 
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Abstract:
      This paper focuses on the study for the stability of stochastic nonlinear programming when the probability measure is perturbed. Under the Lipschitz continuity of the objective function and metric regularity of the feasible set-valued mapping, the outer semicontinuity of the optimal solution set and Lipschitz continuity of optimal values are guaranteed. Importantly, it is proved that, if the linear independence constraint qualification and strong second-order sufficient condition hold at a local minimum point of the original problem, there exists a Lipschitz continuous solution path satisfying the Karush-Kuhn-Tucker conditions.
Citation:
DOI:10.3770/j.issn:2095-2651.2019.03.012
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