Convergence of a Penalty Method for Mathematical Programming with Complementarity Constraints

By X. Hu, D. Ralph. 2004

190 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Control and Systems Engineering, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/14a675ecd64a428583f1128d60a88dda7eee0d8e

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In Computational Theory and Mathematics

In Control and Systems Engineering

In Numerical Analysis

Citations in the corpus

Stationary conditions for mathematical programs with vanishing constraints using weak constraint qualifications (2008, background): “, l, see, for example, the two books [20, 27] for a general treatment and many applications of MPECs, the more recent works [10, 11, 12, 25, 26, 28, 34, 36, 37] for some more refined theoretical results, or [4, 7, 8, 13, 14, 18, 19, 30, 35] for a number of suitable methods.”
An Exact Penalty Method for Binary Optimization Based on MPEC Formulation (2017, background): “It is worthwhile to point out that there are many studies on exact penalty for MPECs (refer to (Luo, Pang, and Ralph, 1996; Hu and Ralph, 2004; Ralph and Wright, 2004; Yuan and Ghanem, 2016b) for examples), but they do not afford the exactness of our penalty problem.”
Annotated Bibliography on Bilevel Programming and Mathematical Programs with Equilibrium Constraints (2003, methodology): “for MPECs in [364], a penalty method in [185] and piece-wise SQP methods [201,268,343,344].”
On M-stationary points for mathematical programs with equilibrium constraints (2005, background): “Later, Hu and Ralph [ 7 ] proved a generalization of this result by showing that a limit point of a whole class of algorithms is an M-stationary point of the MPEC (1).”
Using EPECs to Model Bilevel Games in Restructured Electricity Markets with Locational Prices (2007, methodology): “and Ralph (2001). Further work on EPECs includes the PhD dissertation by Ehrenmann (2004a); various applications in economics by Ehrenmann (2004b), Ehrenmann and Neuhoff (2003), Hu et al.”
On the Guignard constraint qualification for mathematical programs with equilibrium constraints (2005, unknown): “For a more detailed analysis, the reader is referred to the recent papers [3,7,10,19], for example.”