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 …
region of the so-called upper level problem is restricted by the graph of the solution set …
[图书][B] Nonlinear programming techniques for equilibria
In science, the term “equilibrium” has been widely used in physics, chemistry, biology,
engineering, and economics, among others, within different frameworks. It generally refers to …
engineering, and economics, among others, within different frameworks. It generally refers to …
Parallel hybrid extragradient methods for pseudomonotone equilibrium problems and nonexpansive mappings
D Van Hieu, LD Muu, PK Anh - Numerical Algorithms, 2016 - Springer
In this paper we propose and analyze three parallel hybrid extragradient methods for finding
a common element of the set of solutions of equilibrium problems involving …
a common element of the set of solutions of equilibrium problems involving …
[图书][B] Bilevel optimization: theory, algorithms and applications
S Dempe - 2018 - optimization-online.org
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 …
region of the so-called upper level problem is restricted by the graph of the solution set …
[HTML][HTML] Projection algorithms for solving nonmonotone equilibrium problems in Hilbert space
B Van Dinh - Journal of Computational and Applied Mathematics, 2016 - Elsevier
We propose two projection algorithms for solving an equilibrium problem where the
bifunction is not required to be satisfied any monotone property. Under assumptions on the …
bifunction is not required to be satisfied any monotone property. Under assumptions on the …
A projection and contraction method with adaptive step sizes for solving bilevel pseudo-monotone variational inequality problems
In this paper, we propose a single projection method for finding a solution of the bilevel
pseudo-monotone variational inequality problem in real Hilbert spaces. The advantage of …
pseudo-monotone variational inequality problem in real Hilbert spaces. The advantage of …
A projected subgradient algorithm for bilevel equilibrium problems and applications
LQ Thuy, TN Hai - Journal of Optimization Theory and Applications, 2017 - Springer
In this paper, we propose a new algorithm for solving a bilevel equilibrium problem in a real
Hilbert space. In contrast to most other projection-type algorithms, which require to solve …
Hilbert space. In contrast to most other projection-type algorithms, which require to solve …
KKT reformulation and necessary conditions for optimality in nonsmooth bilevel optimization
S Dempe, AB Zemkoho - SIAM Journal on Optimization, 2014 - SIAM
For a long time, the bilevel programming problem has essentially been considered as a
special case of mathematical programs with equilibrium constraints, in particular when the …
special case of mathematical programs with equilibrium constraints, in particular when the …
Relaxed single projection methods for solving bilevel variational inequality problems in Hilbert spaces
In this paper, we first propose a relaxed regularization projection method involving only a
single projection for solving monotone bilevel variational inequality problem in Hilbert …
single projection for solving monotone bilevel variational inequality problem in Hilbert …
Common solutions to pseudomonotone equilibrium problems
DV Hieu - Bulletin of the Iranian Mathematical Society, 2016 - bims.iranjournals.ir
In this paper, we propose two iterative methods for finding a common solution of a finite
family of equilibrium problems for pseudomonotone bifunctions. The first is a parallel hybrid …
family of equilibrium problems for pseudomonotone bifunctions. The first is a parallel hybrid …