Bilevel optimization: theory, algorithms, applications and a bibliography

S Dempe - Bilevel optimization: advances and next challenges, 2020 - Springer
Bilevel optimization problems are hierarchical optimization problems where the feasible
region of the so-called upper level problem is restricted by the graph of the solution set …

Second-order KKT optimality conditions for multiobjective optimal control problems

BT Kien, NV Tuyen, JC Yao - SIAM Journal on Control and Optimization, 2018 - SIAM
In this paper, we study second-order necessary and sufficient optimality conditions of Karush-
-Kuhn--Tucker type for local optimal solutions in the sense of Pareto to a class of …

Optimality conditions for semivectorial bilevel convex optimal control problems

H Bonnel, J Morgan - Computational and Analytical Mathematics: In Honor …, 2013 - Springer
We present optimality conditions for bilevel optimal control problems where the upper level
is a scalar optimal control problem to be solved by a leader and the lower level is a …

Local stability of solutions to a parametric multi-objective optimal control problem

TD Binh, BT Kien, NH Son - Optimization, 2024 - Taylor & Francis
This paper studies local stability of solutions to a parametric multi-objective optimal control
problem with constraints. By combining the scalarization method and non-scalarization …

Semivectorial bilevel convex optimal control problems: existence results

H Bonnel, J Morgan - SIAM Journal on Control and Optimization, 2012 - SIAM
We consider a bilevel optimal control problem where the upper level, to be solved by a
leader, is a scalar optimal control problem, and the lower level, to be solved by several …

[HTML][HTML] Stability Analysis to Parametric Multiobjective Optimal Control Problems

LQ Anh, VT Tai, TN Tam - Journal of Optimization Theory and Applications, 2025 - Springer
In this paper, we investigate continuity properties of the efficient solution map of a parametric
nonlinear multiobjective optimal control problem. First, by using the equimeasurability …

[HTML][HTML] On the second-order optimality conditions for multi-objective optimal control problems with mixed pointwise constraints

BT Kien, TD Binh - Journal of Global Optimization, 2023 - Springer
In this paper, we derive second-order necessary optimality conditions and second-order
sufficient optimality condition for locally Pareto solutions to a class of multi-objective optimal …

Second-order optimality conditions for multiobjective optimal control problems with mixed pointwise constraints and free right end point

BT Kien, X Qin, CF Wen, JC Yao - SIAM Journal on Control and Optimization, 2020 - SIAM
In this paper, we derive first-and second-order necessary optimality conditions of Karush--
Kuhn--Tucker type for H-locally weak solutions in the sense of Pareto of multiobjective …

[HTML][HTML] Post-Pareto analysis and a new algorithm for the optimal parameter tuning of the elastic net

H Bonnel, C Schneider - Journal of Optimization Theory and Applications, 2019 - Springer
The paper deals with the optimal parameter tuning for the elastic net problem. This process
is formulated as an optimization problem over a Pareto set. The Pareto set is associated with …

Doubly nonnegative relaxation method for solving multiple objective quadratic programming problems

YQ Bai, CH Guo - arXiv preprint arXiv:1211.4670, 2012 - arxiv.org
Multicriterion optimization and Pareto optimality are fundamental tools in economics. In this
paper we propose a new relaxation method for solving multiple objective quadratic …