Results 141 to 150 of about 9,354 (201)
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4OR, 2005
This paper provides an introductory survey of a class of optimization problems known as bilevel programming. We motivate this class through a simple application, and then proceed with the general formulation of bilevel programs. We consider various cases (linear, linear-quadratic, nonlinear), describe their main properties and give an overview of ...
Colson, Benoit +2 more
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This paper provides an introductory survey of a class of optimization problems known as bilevel programming. We motivate this class through a simple application, and then proceed with the general formulation of bilevel programs. We consider various cases (linear, linear-quadratic, nonlinear), describe their main properties and give an overview of ...
Colson, Benoit +2 more
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Solving linear fractional bilevel programs
Operations Research Letters, 2004The authors give a geometrical characterization of the optimal solution to the linear fractional bilevel programming (LFBP) problem in terms of what is called a boundary feasible extreme point. It is assumed that the second level optimal solution sets are singletons. The results extend the characterization proved by \textit{Y. H. Liu} and \textit{S. M.
Calvete, Herminia I., Galé, Carmen
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Bilevel convex programming models
Optimization, 2009Bilevel convex models are studied after being cast into a parametric programming form. This form has a lexicographic inner-outer structure where the optimal value of the outer model is optimized on the set of optimal solutions of the inner model. Optimal solutions are characterized using a Lagrangian saddle-point approach and a marginal value formula ...
Trujillo-Cortez, R., Zlobec, Sanjo
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Computers & Operations Research, 1993
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1999
A problem where an optimization problem is constrained by another one is classified as a BiLevel Programming Problem, BLPP, and is of the general form: $$ \begin{array}{l} \mathop {\min }\limits_{x,y} \quad F(x,y) \\ s.t. \\ \quad \quad \;G(x,y) \le 0 \\ \quad \quad \;H(x,y) = 0 \\ \quad \quad \;\mathop {\min }\limits_y f(x,y) \\ \quad \quad \;s.t.
Christodoulos A. Floudas +8 more
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A problem where an optimization problem is constrained by another one is classified as a BiLevel Programming Problem, BLPP, and is of the general form: $$ \begin{array}{l} \mathop {\min }\limits_{x,y} \quad F(x,y) \\ s.t. \\ \quad \quad \;G(x,y) \le 0 \\ \quad \quad \;H(x,y) = 0 \\ \quad \quad \;\mathop {\min }\limits_y f(x,y) \\ \quad \quad \;s.t.
Christodoulos A. Floudas +8 more
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On bilevel fractional programming
Optimization, 1995The bilevel fractional programming problem (BFPP), in which the follower's objective function is a linear fractional functional, is introduced and studied in this paper. The leader's and the follower's decision variables are related by linear constraints.
K. Mathur, M. C. Puri
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2015
The task to find a best point within the set of optimal solutions of a convex optimization problem is called simple bilevel optimization problem. In general, a necessary optimality condition for a convex simple bilevel problem does not need to be sufficient.
Stephan Dempe +3 more
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The task to find a best point within the set of optimal solutions of a convex optimization problem is called simple bilevel optimization problem. In general, a necessary optimality condition for a convex simple bilevel problem does not need to be sufficient.
Stephan Dempe +3 more
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On the Quasiconcave Bilevel Programming Problem
Journal of Optimization Theory and Applications, 1998zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Calvete, H. I., Galé, C.
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Nonlinear integer bilevel programming
European Journal of Operational Research, 1994A lot of practical problems can be formulated as a multi-level programming problem. It contains a sequence of objective functions and everyone of them must be optimized on a part of the variables. The paper presents an algorithm for so-called separable integer monotone bilevel programming problems. A numerical example is given.
Jan, Rong-Hong, Chern, Maw-Sheng
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1998
Of the algorithms presented in Chapter 5 for finding global minima of linear bilevel programs, the Kuhn-Tucker approach [B11], the variable elimination method [H1], and the complementarity approach [J4] are the most efficient and robust developed to date. These algorithms can be readily extended to solve the linear-quadratic case where the functions F,
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Of the algorithms presented in Chapter 5 for finding global minima of linear bilevel programs, the Kuhn-Tucker approach [B11], the variable elimination method [H1], and the complementarity approach [J4] are the most efficient and robust developed to date. These algorithms can be readily extended to solve the linear-quadratic case where the functions F,
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