Funding agency | Austrian Science Fund (FWF) |
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Project number | P 29190 |

Principal investigator | Helmut Gfrerer |

Project employees | Matuš Benko Michael Mandlmayr |

Duration | 2016-10-01 – 2021-09-30 |

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.

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