[图书][B] Variational analysis and applications

BS Mordukhovich - 2018 - Springer
Boris S. Mordukhovich Page 1 Springer Monographs in Mathematics Boris S. Mordukhovich
Variational Analysis and Applications Page 2 Springer Monographs in Mathematics Editors-in-Chief …

Bilevel programming problems

S Dempe, V Kalashnikov, GA Pérez-Valdés… - Energy Systems …, 2015 - Springer
Bilevel optimization is a vital field of active research. Depending on its formulation it is part of
nonsmooth or nondifferentiable optimization, conic programming, optimization with …

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 …

The bilevel programming problem: reformulations, constraint qualifications and optimality conditions

S Dempe, AB Zemkoho - Mathematical Programming, 2013 - Springer
We consider the bilevel programming problem and its optimal value and KKT one level
reformulations. The two reformulations are studied in a unified manner and compared in …

Necessary optimality conditions in pessimistic bilevel programming

S Dempe, BS Mordukhovich, AB Zemkoho - Optimization, 2014 - Taylor & Francis
This article is devoted to the so-called pessimistic version of bilevel programming programs.
Minimization problems of this type are challenging to handle partly because the …

On the Karush–Kuhn–Tucker reformulation of the bilevel optimization problem

S Dempe, AB Zemkoho - Nonlinear Analysis: Theory, Methods & …, 2012 - Elsevier
This paper is mainly concerned with the classical KKT reformulation and the primal KKT
reformulation (also known as an optimization problem with generalized equation constraint …

Holder metric subregularity with applications to proximal point method

G Li, BS Mordukhovich - SIAM Journal on Optimization, 2012 - SIAM
This paper is mainly devoted to the study and applications of Hölder metric subregularity
(or metric q-subregularity of order q∈(0,1) for general set-valued mappings between infinite …

On the solution of convex bilevel optimization problems

S Dempe, S Franke - Computational Optimization and Applications, 2016 - Springer
An algorithm is presented for solving bilevel optimization problems with fully convex lower
level problems. Convergence to a local optimal solution is shown under certain weak …

Sensitivity analysis for two-level value functions with applications to bilevel programming

S Dempe, BS Mordukhovich, AB Zemkoho - SIAM Journal on Optimization, 2012 - SIAM
This paper contributes to a deeper understanding of the link between a now conventional
framework in hierarchical optimization called the optimistic bilevel problem and its initial …

Proximal point algorithms on Hadamard manifolds: linear convergence and finite termination

J Wang, C Li, G Lopez, JC Yao - SIAM Journal on Optimization, 2016 - SIAM
In the present paper, we consider inexact proximal point algorithms for finding singular
points of multivalued vector fields on Hadamard manifolds. The rate of convergence is …