| Convex operators |
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| Teaching Staff in Charge |
| Prof. NEMETH Alexandru, Ph.D., nemab@math.ubbcluj.ro |
| Aims |
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The investigation of the convex operators is the central question of the vectorial convex analysis. Although a new domain, an extended monography is concerned about it (see the literature). The lectures will cover the background of the domain emphasizing about the subdifferential calculus of the convex operators.
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| Content |
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Will be revisited some fundamental results forom the geometry of convex sets in topological vector spaces. It will be introduced the notion of the convex correspondence. The convex operator is a mapping from a vector space into an ordered vector space satisfying the convexity inequality with respect to the order relation of the adress space. When the adress space is a latticially complete ordered vector space, the convex operators have good subdifferentiability properties, expressed by the Hahn-Banach-Kantorovich theorem. The fully subdifferentiability property is requiring weaker property of the adress space. This property is related with the weak Hahn-Banach extension property and is valid for ordered regular topological vector spaces. All these questions will be covered by the course. |
| References |
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1. A.G. Kusraev, S.S. Kutateladze: Subdifferencial'nye iscislenie, Novosibirsk, 1983.
2. A.G. Kusraev, S.S. Kutateladze: Subdifferentials: Theory and Applications, Kluwer, Doderecht, 1995. 3. A.B. Nemeth: Convex operators: Some subdifferentiability results, Optimization, 1992, Vol 23, pp. 275-301. |
| Assessment |
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Exam. |