Bounded Lagrange multiplier rules for general nonsmooth problems and application to mathematical programs with equilibrium constraints

Nooshin Movahedian ()
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Nooshin Movahedian: University of Isfahan

Journal of Global Optimization, 2017, vol. 67, issue 4, No 6, 829-850

Abstract: Abstract In this paper, a general optimization problem is considered to investigate the conditions which ensure the existence of Lagrangian vectors with a norm not greater than a fixed positive number. In addition, the nonemptiness and boundedness of the multiplier sets together with their exact upper bounds is characterized. Moreover, three new constraint qualifications are suggested that each of them follows a degree of boundedness for multiplier vectors. Several examples at the end of the paper indicate that the upper bound for Lagrangian vectors is easily computable using each of our constraint qualifications. One innovation is introducing the so-called bounded Lagrangian constraint qualification which is stated based on the nonemptiness and boundedness of all possible Lagrangian sets. An application of the results for a mathematical program with equilibrium constraints is presented.

Keywords: Optimization problem; Nonsmooth analysis; Lagrange multipliers; Lipschitz-like; Calmness; Constraint system; Constraint qualification; Metric regularity; Metric subregularity; Mathematical programs with equilibrium constraints; 49J52; 90Cxx; 49J53; 26E25 (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10898-016-0442-4

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