Active-set Newton methods for mathematical programs with vanishing constraints

Izmailov, A. F.; Pogosyan, A. L.

doi:10.1007/s10589-012-9467-x

Cited by 8 publications

(1 citation statement)

References 21 publications

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“…MPVC was first introduced by Achtziger and Kanzow (2008) and has been an important research topic. Several theoretical properties and specific numerical algorithms have been studied by researchers (see, e.g., Benko and Gfrerer, 2017; Hoheisel et al, 2012; Izmailov and Pogosyan, 2012; Izmailov and Solodov, 2009). Our research is the first one to show the equivalent relationship between BLPP and MPVC under some specific conditions.…”

Section: Focus Programming Under the Positive Evaluation Systemmentioning

confidence: 99%

Focus programming: a bi‐level programming approach to static stochastic optimization problems

Guo

Zhu

2023

Int Trans Operational Res

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Static stochastic optimization problems are formulated with the focus theory of choice where the optimal solution is determined as per which solution's focus (the most salient realization of a random vector) is the most preferred. The new formulation that we call the focus programming is a bi‐level programming approach in which the lower‐level program is used to choose the focus of each feasible solution and the upper‐level program is to determine the optimal solution. Since in focus programming models upper‐level and lower‐level programs are maximin or minimax problems, they are nonsmooth and sometimes even nonconvex so that the existing optimization methods cannot solve such bi‐level programming problems. We propose several single‐level reformulation methods for such problems.

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