Multiobjective bilevel optimization
type: Item
instance of: scholarly article
title: Multiobjective bilevel optimization
zbMATH Open document ID: 1198.90347
author: Gabriele Eichfelder
published in: Mathematical Programming. Series A. Series B
publication date: 2010-04-15T00:00:00Z
review text: This paper deals with nonlinear non-convex multi-objective bi-level optimization problems which are discussed using an optimistic approach. The author aims to obtain a good approximation of the feasible set of the upper level function by expressing it as the set of minimal solutions of a multi-objective optimization problem. To solve this problem he applies the scalarization approach of \textit{A. Pascoletti} and \textit{P. Serafini} [J. Optimization Theory Appl. 42, 499--524 (1984; Zbl 0505.90072)]. For generating the approximation mentioned above, the author uses sensitivity results for controlling the parameters of the corresponding scalarization problem adaptively. This sensitivity results are used again for solving the upper level problem in an iterative process. Thus, not only one minimal solution but an approximation of the whole efficient set of the multi-objective bilevel optimization problem is determined. The proposed numerical method (without convexity assumptions) demands twice continuously differentiable functions and appropriate solvers for determining global solutions of the scalar problems. Finally, an academic example and a topological problem arising in an application are solved with an algorithm designed for the case of a bi-criteria lower and upper level problem and a one-dimensional upper level variable.
Mathematics Subject Classification ID: 90C29
Mathematics Subject Classification ID: 90C31
Mathematics Subject Classification ID: 90C59
zbMATH DE Number: 5693204
zbMATH Keywords: multicriteria optimization
zbMATH Keywords: vector optimization
zbMATH Keywords: sensitivity
zbMATH Keywords: bilevel optimization
zbMATH Keywords: two-level optimization
reviewed by: Francisco Guerra Vazquez
describes a project that uses: NBI
MaRDI profile type: Publication
full work available at URL: s10107-008-0259-0
OpenAlex ID: W2071707442
cites work: A bi-level non-linear multi-objective decision making under fuzziness.
cites work: Q3363077
cites work: Practical bilevel optimization. Algorithms and applications
cites work: Semivectorial bilevel optimization problem: penalty approach
cites work: Normal-Boundary Intersection: A New Method for Generating the Pareto Surface in Nonlinear Multicriteria Optimization Problems
cites work: Foundations of bilevel programming
cites work: Annotated Bibliography on Bilevel Programming and Mathematical Programs with Equilibrium Constraints
cites work: Q5668630
cites work: Multicriteria optimization
cites work: Scalarizations for adaptively solving multi-objective optimization problems
cites work: An Adaptive Scalarization Method in Multiobjective Optimization
cites work: Introduction to sensitivity and stability analysis in nonlinear programming
cites work: Gap-free computation of Pareto-points by quadratic scalarizations
cites work: Multicriteria approach to bilevel optimization
cites work: On a Bicriterion Formulation of the Problems of Integrated System Identification and System Optimization
cites work: Multiobjective optimization: survey of methods and industrial applications
cites work: Q4461359
cites work: Multiobjective search algorithm with subdivision technique
cites work: Reference point approximation method for the solution of bicriterial nonlinear optimization problems
cites work: Solution point differentiability without strict complementarity in nonlinear programming
cites work: On min-norm and min-max methods of multi-objective optimization
cites work: Nonlinear multiobjective optimization
cites work: Stackelberg solutions to multiobjective two-level linear programming problems
cites work: A multi-level nonlinear multi-objective decision-making under fuzziness
cites work: Scalarizing vector optimization problems
cites work: Approximation methods in multiobjective programming
cites work: Theory of multiobjective optimization
cites work: Norm-based approximation in bicriteria programming
cites work: Interactive bilevel multi-objective decision making
cites work: Model and interactive algorithm of bi-level multi-objective decision-making with multiple interconnected decision makers
cites work: On two generalizations of Pareto minimality
cites work: A novel approach to bilevel nonlinear programming
cites work: Bilevel and multilevel programming: A bibliography review
DOI: 10.1007/S10107-008-0259-0
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description: scientific article; zbMATH DE number 5693204