New Results on Constraint Qualifications for Nonlinear Extremum Problems and Extensions |
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Authors: | Lei Guo Jin Zhang Gui-Hua Lin |
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Affiliation: | 1. School of Mathematical Sciences, Dalian University of Technology, Dalian, 116024, China 2. Sino-US Global Logistics Institute, Shanghai Jiao Tong University, Shanghai, 200030, China 3. Department of Mathematics and Statistics, University of Victoria, Victoria, BC, V8W?3P4, Canada 4. School of Management, Shanghai University, Shanghai, ?200444, China
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Abstract: | In this paper, we focus on some new constraint qualifications introduced for nonlinear extremum problems in the recent literature. We show that, if the constraint functions are continuously differentiable, the relaxed Mangasarian–Fromovitz constraint qualification (or, equivalently, the constant rank of the subspace component condition) implies the existence of local error bounds for the system of inequalities and equalities. We further extend the new result to the mathematical programs with equilibrium constraints. In particular, we show that the MPEC relaxed (or enhanced relaxed) constant positive linear dependence condition implies the existence of local error bounds for the mixed complementarity system. |
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