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Complementary Problems with Polynomial Data
- Source :
- Vietnam Journal of Mathematics. 49:1283-1303
- Publication Year :
- 2021
- Publisher :
- Springer Science and Business Media LLC, 2021.
-
Abstract
- Given polynomial maps $f, g \colon \mathbb {R}^{n} \to \mathbb {R}^{n}$ , we consider the polynomial complementary problem of finding a vector $x \in \mathbb {R}^{n}$ such that $$ f(x) \ge 0, \quad g(x) \ge 0, \quad \text{ and } \quad \langle f(x), g(x) \rangle = 0. $$ In this paper, we present various properties on the solution set of the problem, including genericity, nonemptiness, compactness, uniqueness as well as error bounds with explicit exponents. These strengthen and generalize some previously known results.
- Subjects :
- Polynomial (hyperelastic model)
021103 operations research
General Mathematics
0211 other engineering and technologies
Solution set
010103 numerical & computational mathematics
02 engineering and technology
90C33
01 natural sciences
Combinatorics
Compact space
Optimization and Control (math.OC)
FOS: Mathematics
Uniqueness
0101 mathematics
Mathematics - Optimization and Control
Mathematics
Subjects
Details
- ISSN :
- 23052228 and 2305221X
- Volume :
- 49
- Database :
- OpenAIRE
- Journal :
- Vietnam Journal of Mathematics
- Accession number :
- edsair.doi.dedup.....daa786575e9935118d4e7877ed94ecf7