Constraint Qualification with Schauder Basis for Infinite Programming Problems
We consider infinite programming problems with constraint sets defined by systems of infinite number of inequalities and equations given by continuously differentiable functions defined on Banach spaces. In the approach proposed here we represent these systems with the help of coefficients in a give...
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| Veröffentlicht in: | Applied mathematics & optimization 2023-10, Vol.88 (2), p.66, Article 66 |
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| creator | Bednarczuk, E. M. Leśniewski, K. W. Rutkowski, K. E. |
| description | We consider infinite programming problems with constraint sets defined by systems of infinite number of inequalities and equations given by continuously differentiable functions defined on Banach spaces. In the approach proposed here we represent these systems with the help of coefficients in a given Schauder basis. We prove Abadie constraint qualification under the new infinite-dimensional Relaxed Constant Rank Constraint Qualification Plus and we discuss the existence of Lagrange multipliers via Hurwicz set. The main tools are: Rank Theorem and Lyusternik–Graves theorem. |
| doi_str_mv | 10.1007/s00245-023-10034-0 |
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| subjects | Applied mathematics Banach spaces Calculus of Variations and Optimal Control Optimization Control Lagrange multiplier Mathematical and Computational Physics Mathematical Methods in Physics Mathematics Mathematics and Statistics Numerical and Computational Physics Optimization Simulation Systems Theory Theorems Theoretical |
| title | Constraint Qualification with Schauder Basis for Infinite Programming Problems |
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