Foundations of Bilevel Programming

By Stephan Dempe. 2002

1,510 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Control and Systems Engineering, Economics and Econometrics

View Paper: https://www.semanticscholar.org/paper/1cfaf749d24ffeb213f4537c36b6b78494a1f7c5

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

In Control and Systems Engineering

In Economics and Econometrics

Citations in the corpus

Stacking sequence and shape optimization of laminated composite plates via a level-set method (2016, background): “This gives rise to a bi-level optimization scheme [20].”
Bilevel Optimization and Machine Learning (2008, background): “The systematic study of the bilevel optimization problem and its MPEC extension attracted the intensive attention of mathematical programmers about a decade ago with the publication of a focused monograph by Luo, Pang and Ralph [4], which was followed by two related monographs [6,7].”
A Bilevel Stochastic Programming Approach for Retailer Futures Market Trading (2009, background): “The problem faced by the retailer can be formulated as a bilevel programming problem [12], i.”
Automated Machine Learning: From Principles to Practices (2018, background): “• Bi-level optimization [31] is a kind of hierarchical optimization where one problem is embedded within another.”
Analysis of the AutoML Challenge Series 2015-2018 (2019, methodology): “As an optimization problem, model selection is a bi-level optimization program (Colson et al., 2007; Dempe, 2002; Bennett et al., 2008); there is a lower objective J1 to train the parameters α of the model, and an upper objective J2 to train the hyper-parameters θ, both optimized simultaneously (see”
Reward Optimization for Neural Machine Translation with Learned Metrics (2021, background): “Bi-level optimization (Dempe, 2002; Colson et al., 2007) is a framework that formulates such a constrained optimization problem.”
An overview of bilevel optimization (2007, background): “The most recent book on bilevel programming, as of May 2005, is that of Dempe (2002) .”
Annotated Bibliography on Bilevel Programming and Mathematical Programs with Equilibrium Constraints (2003, methodology): “For an introduction to the optimistic formulation [117] can be useful.”
Optimality Conditions for a Simple Convex Bilevel Programming Problem (2010, methodology): “For details on these approaches see, for example, Dempe [ 2 ], Dutta and Dempe [10], Dempe et al. [3, 4] and the references there in.”
Is bilevel programming a special case of a mathematical program with complementarity constraints? (2012, background): “Many theoretical results can be found in the monographs Bard [2] and Dempe [4] and the edited volumes Migdalas et al.”
On the solution of convex bilevel optimization problems (2015, neutral): “Bilevel optimization has been the topic of three monographs [1] by Bard, [2] by Dempe and [3] by Dempe et al. as well as of the bibliography [4] by Dempe.”
New necessary optimality conditions in optimistic bilevel programming (2007, background): “Our notation is basically standard; see the books 7 , 12 , 19 .”
Constant-Rank Condition and Second-Order Constraint Qualification (2010, methodology): “The Constant Rank constraint qualification seems to be a useful tool for the analysis of convergence of some nonlinear programming methods, see for example [23, 24, 25].”
A Review on Bilevel Optimization: From Classical to Evolutionary Approaches and Applications (2017, background): “At this point, we would like to refer the readers to other review papers [49], [57], [90], [150], [164] and books [18], [60], [61], [140], [159] on bilevel optimization.”
A bilevel mixed-integer program for critical infrastructure protection planning (2008, methodology): “Decomposition involves the use of cutting plane algorithms and is usually indicated to solve problems with parameter-independent constraints in the lower-level problem [30].”