2001
DOI: 10.1006/jmaa.2000.7001
|View full text |Cite
|
Sign up to set email alerts
|

Existence of Solutions to Two-Level Optimization Problems with Nonunique Lower-Level Solutions

Abstract: In this paper, we consider a two-level optimization problem with nonunique lower-level solutions. We give sufficient conditions ensuring the existence of solutions. ᮊ

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
3
1

Citation Types

2
10
0

Year Published

2008
2008
2020
2020

Publication Types

Select...
5
3

Relationship

2
6

Authors

Journals

citations
Cited by 14 publications
(12 citation statements)
references
References 4 publications
2
10
0
Order By: Relevance
“…For illustration, let us consider the following example where all assumptions of Theorem 3 are satisfied. [1,2] and B = [1,2]. Let F and f be the functions defined on R 2 × R × R and R 2 × R respectively by Then, z = 1 is a common solution to the problems P(x) and Q(x, y).…”
Section: Remarkmentioning
confidence: 99%
See 2 more Smart Citations
“…For illustration, let us consider the following example where all assumptions of Theorem 3 are satisfied. [1,2] and B = [1,2]. Let F and f be the functions defined on R 2 × R × R and R 2 × R respectively by Then, z = 1 is a common solution to the problems P(x) and Q(x, y).…”
Section: Remarkmentioning
confidence: 99%
“…Set C = x ∈ R n / f i (x) ≤ 0, i = 1, ...m} and θ(x) = (f + 1 (x), ..., f + m (x)), with f + i (x) = max(0, f i (x)), i = 1, ..., m. Auslender and Crouzeix in [7] have been interested by the best constant denoted by k 2,∞ that satisfies 2 and . ∞ denote respectively the euclidean norm on R n and the Tchebycheff norm on R m .…”
Section: Introductionmentioning
confidence: 99%
See 1 more Smart Citation
“…As a result, it is difficult to determine the leader's solution. That is the reason why we use the quotation marks in problems (1)- (2). To overcome this situation, the majority of authors used optimistic formulation and pessimistic formulation, which represented the two extreme situations between the leader and the follower.…”
Section: Introductionmentioning
confidence: 99%
“…Note that such a class of nonlinear bilevel problems presents a major difficulty in finding sufficient conditions that ensure the existence of solutions (comments and an exhaustive list are given in [9]). Sufficient condition for the existence of solutions to weak bilevel problems are given in [1][2][3]16]. Finally, we give some cases where the property (P) introduced for Min Sup problems is satisfied.…”
Section: Introductionmentioning
confidence: 99%