Regularity and Stability for Generalized Equations

Funding agency	Austrian Science Fund (FWF)
Project number	P 29190
Principal investigator	Helmut Gfrerer
Project employees	Matuš Benko Michael Mandlmayr
Duration	2016-10-01 – 2021-09-30

Description

Setting up equations and solving them has been for a long time one of the most important problems of mathematics. Nowadays models have evolved beyond equations and mathematical models resting on equations are replaced by "generalized equations" models.

The key concept for working at this general level is that of a set-valued mapping, which assigns to each point in the domain a set of values, and not only one value like an ordinary function. This leads to the replacement of the equality sign in equations by an inclusion in generalized equation. Wide fields of application are provided by problems of minimizing or maximizing functions subject to constraints or by models of competitive equilibrium.

Publications

H. Gfrerer, B.S. Mordukhovich
Robinson stability of parametric constraint systems via variational analysis
SIAM J. Optim. 27 (2017), pp. 438-465
doi
H. Gfrerer, J.J. Ye
New constraint qualifications for mathematical programs with equilibrium constraints via variational analysis
SIAM J. Optim. 27 (2017), pp. 842-865
doi accepted manuscript
H. Gfrerer, J. Outrata
On the Aubin property of a class of parameterized variational systems
Math. Meth. Oper. Res. 86 (2017), pp. 443-467
doi accepted manuscript
M. Benko, H. Gfrerer
New verifiable stationarity concepts for a class of mathematical programs with disjunctive constraints
Optimization 67 (2018), pp. 1-23
doi
H. Gfrerer, B.S. Mordukhovich
Second-Order Variational Analysis of Parametric Constraint and Variational Systems
SIAM J. Optim. 29 (2019), pp. 423–453
doi accepted manuscript
M. Benko, H. Gfrerer, B.S. Mordukhovich
Characterizations of Tilt-Stable Minimizers in Second-Order Cone Programming
SIAM J. Optim. 29 (2019), pp. 3100–3130
doi accepted manuscript
H. Gfrerer, J. Outrata
On the Aubin property of solution maps to parameterized variational systems with implicit constraints
Optimization 69 (2019), pp. 1681-2701
doi
M. Benko, H. Gfrerer, J.V. Outrata
Calculus for Directional Limiting Normal Cones and Subdifferentials
Set-Valued Var. Anal. 27 (2019), pp. 713-745
doi
H. Gfrerer
Linearized M-stationarity Conditions for General Optimization Problems
Set-Valued Var. Anal. 27 (2019), pp. 819-840
doi accepted manuscript
A.L. Dontchev, H. Gfrerer, A.Y. Kruger, J.V. Outrata
The Radius of Metric Subregularity
Set-Valued Var. Anal. 28 (2020), pp.451-473
doi accepted manuscript
M. Benko, H. Gfrerer, J.V. Outrata
Stability Analysis for Parameterized Variational Systems with Implicit Constraints
Set-Valued Var. Anal. 28 (2020), pp. 167-193
doi
H. Gfrerer, J.J. Ye
New Sharp Necessary Optimality Conditions for Mathematical Programs with Equilibrium Constraints
Set-Valued Var. Anal. 28 (2020), pp. 395-426
doi accepted manuscript
H. Gfrerer, J. Outrata, J. Valdman
On the application of the semismooth* Newton method to variational inequalities of the second kind
Technical report (2020)
arxiv
H. Gfrerer, J. Outrata
On a Semismooth* Newton Method for Solving Generalized Equations
SIAM J. Optim. 31 (2021), pp. 489-517
doi accepted manuscript
H. Gfrerer, J.V. Outrata, J. Valdman
On the application of the SCD semismooth* Newton method to variational inequalities of the second kind
Technical report (2021), submitted
arxiv
H. Gfrerer, J.V. Outrata
On (local) analysis of multifunctions via subspaces contained in graphs of generalized derivatives
J. Math. Anal. Appl. 508 (2022)
doi
H. Gfrerer, J.J. Ye, J. Zhou
Second-Order Optimality Conditions for Nonconvex Set-Constrained Optimization Problems
Meth. Oper. Res. (2022)
doi accepted manuscript