Journal ArticleDOI
An explicit solution to the multi-level programming problem
Jonathan F. Bard,James E. Falk +1 more
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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.About:
This article is published in Computers & Operations Research.The article was published on 1982-01-01. It has received 493 citations till now. The article focuses on the topics: Cutting stock problem & Optimization problem.read more
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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 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.
Journal ArticleDOI
Bilevel and multilevel programming: A bibliography review
TL;DR: This paper contains a bibliography of all references central to bilevel and multilevel programming that the authors know of and it is hoped that this bibliography facilitates and encourages their research.
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.
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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.
References
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Book ChapterDOI
Non-cooperative games
TL;DR: In this article, it was shown that the set of equilibrium points of a two-person zero-sum game can be defined as a set of all pairs of opposing "good" strategies.
Book
Nonlinear Programming: Sequential Unconstrained Minimization Techniques
TL;DR: This report gives the most comprehensive and detailed treatment to date of some of the most powerful mathematical programming techniques currently known--sequential unconstrained methods for constrained minimization problems in Euclidean n-space--giving many new results not published elsewhere.
Journal ArticleDOI
Equilibrium Points of Bimatrix Games
C. E. Lemke,J. T. Howson +1 more
TL;DR: An algebraic proof of the existence of equilibrium points for two-person non-zero-sum games is given in this paper, leading to an efficient scheme for computing an equilibrium point, which is valid for any ordered field.
Journal ArticleDOI
Bimatrix Equilibrium Points and Mathematical Programming
TL;DR: In this paper, simple constructive proofs are given of solutions to the matric matric system Mz − ω = q; z ≧ 0; ω ≧ 1; zT = 0, for various kinds of data M, q, which embrace quadratic programming and the problem of finding equilibrium points of bimatrix games.