Abstract
We consider quasi-variational inequality problems (QVI) given by polynomial functions. By applying Lagrange multiplier expressions, we formulate polynomial optimization problems whose minimizers are KKT points for the QVI. Then, feasible extensions are exploited to preclude KKT points that are not solutions. Moment-SOS relaxations are incorporated to solve the polynomial optimization problems in our methods. Under certain conditions, our approach guarantees to find a solution to the QVI or detect the nonexistence of solutions.
| Original language | English |
|---|---|
| Pages (from-to) | 61-83 |
| Number of pages | 23 |
| Journal | Numerical Algebra, Control and Optimization |
| Volume | 16 |
| Early online date | 9 Dec 2024 |
| DOIs | |
| Publication status | Published - 31 Mar 2026 |
Funding
Xindong Tang is supported by the NSFC Young Scientists Fund, grant number [12301407]. Min Zhang is supported by the National Natural Science Foundation of China Youth Fund Project, grant number [12101598].
Keywords
- Lagrange multiplier expression
- Moment-SOS hierarchy
- polynomial optimization
- Quasi-variational inequality
ASJC Scopus subject areas
- Algebra and Number Theory
- Control and Optimization
- Applied Mathematics
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