Necessary optimality conditions for semi-vectorial bi-level optimization with convex lower level: theoretical results and applications to the quadratic case

DOI10.1007/s40305-020-00305-wzbMath1488.90132OpenAlexW3043718207MaRDI QIDQ2059178

Julien Collonge

Publication date: 13 December 2021

Published in: Journal of the Operations Research Society of China (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s40305-020-00305-w

zbMATH Keywords

multi-objective optimizationquadratic optimizationbi-level optimizationmulti-objective convex optimizationpost-Pareto optimization

Mathematics Subject Classification ID

Convex programming (90C25) Nonconvex programming, global optimization (90C26) Multi-objective and goal programming (90C29) Nonlinear programming (90C30) Quadratic programming (90C20)

Cites Work

• Optimality conditions for pessimistic semivectorial bilevel programming problems
• Solving ill-posed bilevel programs
• Stochastic optimization over a Pareto set associated with a stochastic multi-objective optimization problem
• Optimization over the efficient set: overview
• Optimization over the efficient set of multi-objective convex optimal control problems
• Convex functions, monotone operators and differentiability.
• Minimization of a quasi-concave function over an efficient set
• Semivectorial bilevel optimization on Riemannian manifolds
• Multiobjective bilevel optimization
• An exact penalty on bilevel programs with linear vector optimization lower level
• A theoretical approximation scheme for Stackelberg problems
• Multiple-criteria decision making. Concepts, techniques, and extensions. With the assistance of Yoon-Ro Lee and Antonie Stam
• Proper efficiency with respect to cones
• Further analysis of an outcome set-based algorithm for multiple-objective linear programming
• Hybrid approach for solving multiple-objective linear programs in outcome space
• An outer approximation algorithm for generating all efficient extreme points in the outcome set of a multiple objective linear programming problem
• Nonlinear multiobjective optimization
• A finite, nonadjacent extreme-point search algorithm for optimization over the efficient set
• Necessary conditions for nonlinear suboptimization over the weakly- efficient set
• Stability of regularized bilevel programming problems
• Generating the efficient outcome set in multiple objective linear programs: The bicriteria case
• Variational methods in partially ordered spaces
• Multicriteria optimization
• Foundations of bilevel programming
• Weak via strong Stackelberg problem: New results
• Maximizing a concave function over the efficient or weakly-efficient set
• Outcome-based algorithm for optimizing over the efficient set of a bicriteria linear programming problem
• Dual approach to minimization on the set of Pareto-optimal solutions
• New optimality conditions for the semivectorial bilevel optimization problem
• A solution method for semivectorial bilevel programming problem via penalty method
• A novel penalty function method for semivectorial bilevel programming problem
• Optimization over the Pareto outcome set associated with a convex bi-objective optimization problem: theoretical results, deterministic algorithm and application to the stochastic case
• Optimality conditions for minimization over the (weakly or properly) efficient set
• Semivectorial bilevel optimization problem: penalty approach
• On optimization over the efficient set in linear multicriteria programming
• Vector optimization. Set-valued and variational analysis.
• Proper efficiency and the theory of vector maximization
• Numerical solution for optimization over the efficient set by d.c. optimization algorithms
• A global solution method for semivectorial bilevel programming problem
• Optimization over the efficient set using an active constraint approach
• BOND PORTFOLIO OPTIMIZATION BY BILINEAR FRACTIONAL PROGRAMMING
• Annotated Bibliography on Bilevel Programming and Mathematical Programs with Equilibrium Constraints
• Algorithms for the vector maximization problem
• Semivectorial Bilevel Convex Optimal Control Problems: Existence Results
• Semivectorial bilevel programming versus scalar bilevel programming
• New necessary optimality conditions in optimistic bilevel programming
• Optimality Conditions for Semivectorial Bilevel Convex Optimal Control Problems
• Optimization over the efficient set
• Optimization over the efficient set
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Necessary optimality conditions for semi-vectorial bi-level optimization with convex lower level: theoretical results and applications to the quadratic case