New Results on Constraint Qualifications for Nonlinear Extremum Problems and Extensions

Lei Guo (), Jin Zhang () and Gui-Hua Lin ()
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Lei Guo: Dalian University of Technology
Jin Zhang: University of Victoria
Gui-Hua Lin: Shanghai University

Journal of Optimization Theory and Applications, 2014, vol. 163, issue 3, No 4, 737-754

Abstract: 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.

Keywords: Nonlinear extremum problem; Constraint qualification; Error bound; Mathematical program with equilibrium constraints; 90C30; 90C33; 90C46 (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (5)

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DOI: 10.1007/s10957-013-0510-6

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