Journal ArticleDOI
The steepest descent direction for the nonlinear bilevel programming problem
Gilles Savard,Jacques Gauvin +1 more
TLDR
In this article, the authors give necessary optimality conditions for the nonlinear bilevel programming problem and show that the steepest descent direction is obtained by solving a quadratic BLEP.About:
This article is published in Operations Research Letters.The article was published on 1994-06-01. It has received 149 citations till now. The article focuses on the topics: Bilevel optimization & Method of steepest descent.read more
Citations
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Journal ArticleDOI
An overview of bilevel optimization
TL;DR: This paper presents fields of application, focus on solution approaches, and makes the connection with MPECs (Mathematical Programs with Equilibrium Constraints), a branch of mathematical programming of both practical and theoretical interest.
Journal ArticleDOI
A Review on Bilevel Optimization: From Classical to Evolutionary Approaches and Applications
TL;DR: A comprehensive review on bilevel optimization from the basic principles to solution strategies is provided in this paper, where a number of potential application problems are also discussed and an automated text-analysis of an extended list of papers has been performed.
Journal ArticleDOI
Bilevel programming: A survey
TL;DR: An introductory survey of a class of optimization problems known as bilevel programming, which considers various cases (linear, linear-quadratic, nonlinear), describe their main properties and give an overview of solution approaches.
Journal ArticleDOI
Annotated Bibliography on Bilevel Programming and Mathematical Programs with Equilibrium Constraints
TL;DR: In this bibliography main directions of research as well as main fields of applications of bilevel programming problems and mathematical programs with equilibrium constraints are summarized.
Posted Content
A Review on Bilevel Optimization: From Classical to Evolutionary Approaches and Applications.
TL;DR: An automated text-analysis of an extended list of papers published on bilevel optimization from the basic principles to solution strategies; both classical and evolutionary is performed.
References
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Journal ArticleDOI
A Representation and Economic Interpretation of a Two-Level Programming Problem
TL;DR: A solution procedure is developed that replaces the subproblem by its Kuhn-Tucker conditions and then further transforms it into a mixed integer quadratic programming problem by exploiting the disjunctive nature of the complementary slackness conditions.
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Two-Level Linear Programming
Wayne F. Bialas,Mark H. Karwan +1 more
TL;DR: This paper examines the special case of the two-level linear programming problem and presents geometric characterizations and algorithms to demonstrate the tractability of such problems and motivate a wider interest in their study.
Journal ArticleDOI
An explicit solution to the multi-level programming problem
Jonathan F. Bard,James E. Falk +1 more
TL;DR: The bi-level linear case is addressed in detail and the reformulated optimization problem is linear save for a complementarity constraint of the form 〈u, g〉 = 0.
Journal ArticleDOI
New branch-and-bound rules for linear bilevel programming
TL;DR: In this paper, a branch-and-bound algorithm for linear bilevel programming is proposed, where necessary optimality conditions expressed in terms of tightness of the follower's constraints are used to fathom or simplify subproblems, branch and obtain penalties similar to those used in mixed-integer programming.