Sufficient conditions for the existence of multipliers and Lagrangian duality in abstract optimization problems
| Autor: | E. V. Tamminen |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 1994 |
| Předmět: |
Pure mathematics
Control and Optimization Optimization problem Karush–Kuhn–Tucker conditions Applied Mathematics Duality (mathematics) Mathematical analysis Management Science and Operations Research symbols.namesake Lagrange multiplier Theory of computation symbols Strong duality Multiplier (economics) Mathematics Vector space |
| Zdroj: | Tamminen, E 1994, ' Sufficient conditions for the existence of multipliers and Lagrangian duality in abstract optimization problems ', Journal of Optimization Theory and Applications, vol. 82, no. 1, pp. 93-104 . https://doi.org/10.1007/BF02191781 |
| DOI: | 10.1007/BF02191781 |
| Popis: | We consider the following optimization problem: in an abstract set X, find and element x that minimizes a real function f subject to the constraints g(x)≤0 and h(x)=0, where g and h are functions from X into normed vector spaces. Assumptions concerning an overall convex structure for the problem in the image space, the existence of interior points in certain sets, and the normality of the constraints are formulated. A theorem of the alternative is proved for systems of equalities and inequalities, and an intrinsic multiplier rule and a Lagrangian saddle-point theorem (strong duality theorem) are obtained as consequences. |
| Databáze: | OpenAIRE |
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