Local Convergence of SQP Methods for Mathematical Programs with Equilibrium Constraints

By Roger Fletcher, Sven Leyffer, D. Ralph, Stefan Scholtes. SIAM Journal on Optimization, 2006

299 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/6a8f0cbff23ef7ed6ad2807a6a91c36048496a62

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In Computational Theory and Mathematics

In Control and Systems Engineering

In Numerical Analysis

Citations in the corpus

Quasi-variational inequalities, generalized Nash equilibria, and multi-leader-follower games (2009, background): “Taking this implied bound into consideration (which is redundant in the full formulation below), firm I's problem is then stated as the following MPEC: For fixed but arbitrary ρ II ∈ [0, 1], determine ρ I , q I,I , q I,II , γ I,I , and γ I,II to maximize ρ I q I,I subject to 0 ≤ ρ I ≤ 1 0 ≤ q I,I ⊥ ”
A direct method for trajectory optimization of rigid bodies through contact (2014, unknown): “While these are generally difficult to solve, significant research has been directed in this area, and we leverage Sequential Quadratic Programming (SQP) techniques—a particular class of algorithms for solving general nonlinear programs that have been shown to be effective (Anitescu, 2005; Fletcher ”
Complementarity constraints as nonlinear equations: Theory and numerical experience (2006, methodology): “In this paper, we extend our results of [17] by considering NLP formulations of (1.”
Equilibria in an Oligopolistic Electricity Pool With Stepwise Offer Curves (2012, background): “2) The MFCQ does not hold at any feasible solution which implies that the multipliers set at any stationarity points is unbounded, forms a ray, and is not unique [5].”
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.”
On M-stationary points for a stochastic equilibrium problem under equilibrium constraints in electricity spot market modeling (2007, unknown): “We refer to the monographs [14, 19, 5], the survey [12] and to [25, 6].”
An overview of bilevel optimization (2007, methodology): “For instance, filter methods have been used by Fletcher and Leyffer (2002b), while sequential quadratic programming approaches have been proposed by Jian and Ralph (1997), Ralph (1998) and Fletcher et al. (2002) .”
An SOS1-Based Approach for Solving MPECs with a Natural Gas Market Application (2013, background): “Some recent examples include works by Fletcher and Leyffer (2004); Fletcher et al. 2006); Leyffer et al. (2006), and Anitescu et al. (2007) that search for stationary points of these problems.”
Using EPECs to Model Bilevel Games in Restructured Electricity Markets with Locational Prices (2007, methodology): “See Fletcher et al. (2002), Scheel and Scholtes (2000) for related discussions of stationarity conditions in MPECs.”