Second order sufficient conditions for aclass of bilevel programs with lower level second-order coneprogramming problem
Xiaoni Chi, Zhongping Wan, Zijun Hao · Journal of Industrial and Management Optimization · 2015
When there is uncertainty in the lower level optimization problem ofa bilevel programming, it can be formulated by a robust optimizationmethod as a bilevel program with lower level second-order coneprogramming problem (SOCBLP). In this paper, we show that theLagrange multiplier set mapping of the lower level problem of aclass of the SOCBLPs is upper semicontinuous under suitableassumptions. Based on this fact, we detect the similarities andrelationships between the SOCBLP and its KKT reformulation. Then wederive the specific expression of the critical cone at a feasiblepoint, and show that the second order sufficient conditions aresufficient for the second order growth at an M-stationary point ofthe SOCBLP under suitable conditions.