Details
| Original language | English |
|---|---|
| Pages (from-to) | 560-575 |
| Number of pages | 16 |
| Journal | Optimization Methods and Software |
| Volume | 35 |
| Issue number | 3 |
| Publication status | Published - 22 Mar 2019 |
Abstract
We show that the problem of unconstrained minimization of a function in abs-normal form is equivalent to identifying a certain stationary point of a counterpart Mathematical Program with Equilibrium Constraints (MPEC). Hence, concepts introduced for the abs-normal forms turn out to be closely related to established concepts in the theory of MPECs. We give a number of proofs of equivalence or implication for the kink qualifications LIKQ and MFKQ. We also show that the counterpart MPEC always satisfies MPEC-ACQ. We then consider non-smooth nonlinear optimization problems (NLPs) where both the objective function and the constraints are presented in the abs-normal form. We show that this extended problem class also has a counterpart MPEC problem.
Keywords
- 90C30, 90C33, 90C46, abs-normal form, constraint qualifications, MPECs, Non-smooth optimization, stationarity conditions
ASJC Scopus subject areas
- Computer Science(all)
- Software
- Mathematics(all)
- Control and Optimization
- Mathematics(all)
- Applied Mathematics
Cite this
- Standard
- Harvard
- Apa
- Vancouver
- BibTeX
- RIS
In: Optimization Methods and Software, Vol. 35, No. 3, 22.03.2019, p. 560-575.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - On the relation between MPECs and optimization problems in abs-normal form
AU - Hegerhorst-Schultchen, Lisa Christine
AU - Kirches, C.
AU - Steinbach, Marc C.
N1 - Funding information: C. Kirches was supported by the German Federal Ministry of Education and Research (Bundesministerium für Bildung und Forschung) [grant nos 05M17MBA-MoPhaPro, 05M18MBA-MOReNet, 01/S17089C-ODINE] and by Deutsche Forschungsgemeinschaft (DFG) through Priority Programme 1962 [grant no. KI1839/1-1] (http://gepris.dfg.de/gepris/projekt/314147871). The authors thank Andreas Griewank and Andrea Walther for prolific discussions of material related to this article.
PY - 2019/3/22
Y1 - 2019/3/22
N2 - We show that the problem of unconstrained minimization of a function in abs-normal form is equivalent to identifying a certain stationary point of a counterpart Mathematical Program with Equilibrium Constraints (MPEC). Hence, concepts introduced for the abs-normal forms turn out to be closely related to established concepts in the theory of MPECs. We give a number of proofs of equivalence or implication for the kink qualifications LIKQ and MFKQ. We also show that the counterpart MPEC always satisfies MPEC-ACQ. We then consider non-smooth nonlinear optimization problems (NLPs) where both the objective function and the constraints are presented in the abs-normal form. We show that this extended problem class also has a counterpart MPEC problem.
AB - We show that the problem of unconstrained minimization of a function in abs-normal form is equivalent to identifying a certain stationary point of a counterpart Mathematical Program with Equilibrium Constraints (MPEC). Hence, concepts introduced for the abs-normal forms turn out to be closely related to established concepts in the theory of MPECs. We give a number of proofs of equivalence or implication for the kink qualifications LIKQ and MFKQ. We also show that the counterpart MPEC always satisfies MPEC-ACQ. We then consider non-smooth nonlinear optimization problems (NLPs) where both the objective function and the constraints are presented in the abs-normal form. We show that this extended problem class also has a counterpart MPEC problem.
KW - 90C30
KW - 90C33
KW - 90C46
KW - abs-normal form
KW - constraint qualifications
KW - MPECs
KW - Non-smooth optimization
KW - stationarity conditions
UR - http://www.scopus.com/inward/record.url?scp=85063237534&partnerID=8YFLogxK
U2 - 10.1080/10556788.2019.1588268
DO - 10.1080/10556788.2019.1588268
M3 - Article
AN - SCOPUS:85063237534
VL - 35
SP - 560
EP - 575
JO - Optimization Methods and Software
JF - Optimization Methods and Software
SN - 1055-6788
IS - 3
ER -