2020/05/14 by Patrick Mehlitz, Mehlitz, Patrick, Л. И. Минченко +1
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · #49J53 #90C30 #90C31 #Advanced Optimization Algorithms Research #FOS: Mathematics #Optimization and Control (math.OC) #Optimization and Variational Analysis #Peroxisome Proliferator-Activated Receptors
paper · pdf · doi:10.48550/arxiv.2005.06768
openalex publication_date 2020/05/14 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28
The presence of Lipschitzian properties for solution mappings associated with\nnonlinear parametric optimization problems is desirable in the context of\nstability analysis or bilevel optimization. An example of such a Lipschitzian\nproperty for set-valued mappings, whose graph is the solution set of a system\nof nonlinear inequalities and equations, is R-regularity. Based on the\nso-called relaxed constant positive linear dependence constraint qualification,\nwe provide a criterion ensuring the presence of the R-regularity property. In\nthis regard, our analysis generalizes earlier results of that type which\nexploited the stronger Mangasarian-Fromovitz or constant rank constraint\nqualification. Afterwards, we apply our findings in order to derive new\nsufficient conditions which guarantee the presence of R-regularity for solution\nmappings in parametric optimization. Finally, our results are used to derive an\nexistence criterion for solutions in pessimistic bilevel optimization and a\nsufficient condition for the presence of the so-called partial calmness\nproperty in optimistic bilevel optimization.\n